This is discussed in Habitable Planets for Man, Stephen H. Dole, 1964.
Starting on page 67 Dole discusses the upper mass limits for the star of a habitable planet. Above a certain mass, a star will not stay on the main sequence long enough for a planet to develop a brathable atmosphere. Dole then discusses the lower limits of mass for a star which can have a human habitable planet.
The less massive a main sequence star is, the less luminous it is, and so a habitable world with habitable temperatures would have to orbit closer. Below a certain stellar mass the luminosity is so low that a planet orbiting in the circumstellar habitable zone (which Dole calls the "ecosphere") would suffer such strong tidal forces from the star that it would be tidally locked.
Dole discusses the lower limits of mass due to tidal braking forces on pages 68 to 72. On pages 71 to 72, Dole writes:
As may be seen from figure 26, if h2 equal to 2.0 is used as a criterion, habitable planets can exist in ecospheres only around stars having masses larger than 0.72 solar mass. A "full" ecosphere can exist around primaries of stella rmass greater than about 0.88 solar mass, but the ecosphere is narrowed by the tidal braking effect for primaries of lesser mass until it disappears when the stellar mass reaches about 0.72.
The range in mass of stars that could have habitable planets is thus 0.72 to 1.43 solar masses, corresponding cto main sequence stars of spectral classes F2 to K1. There is an extension of this range down to the larger class M stars (mass greater than 0.35 solar mass) for a special class of planets with large satellites. This will be discussed in the next section.
According to this chart, a class F3V star has a mass of 1.44 solar masses:
According to the chart here a K0V type star has a mass of 0.88 solar masses:
This may reflect more accurate knowledge of the masses and spectral types of stars since Dole wrote.
In the next section Dole writes on pages 72 & 73:
The tidal barking forces of a primary also apply to satellites. If h2 of a satellite on a planet is greater than 2.0 but that of the primary is less than 2.0, one would expect to find the planet's rotation halted with respect to the satellite but continuing with respect to the primary. The planet's solar day and synodic month would thus be of the same length. For this condition to be compatible with habitability, however, the period would have to be such as to produce a solar day less than 96 hours in duration--a figure rather arbitrarily chosen as thelongest day for habitability.
And Dole goes on to discuss calculating the tidal forces of the satellite and the primary on a planet.
On page 74 Dole writes:
It is interesting to note that within a certain range of satellite masses twin habitable planets that did not rotate with respect to each other could exist.
So according to Dole the satellite could be as large as the planet. And he goes o to write:
The right hand portion of figure 28 rpesents the situation in which the satellite is larger than the habitable planet.
Which of course makes the habitable "planet" really the satellite or moon, and the more massive "satellite" actually the planet.
In recent decades there has been much discussion of the possibility that very large exomoons orbiitng giant exoplanets that orbit in the circumstellar habitable zones of their stars could be habitable. Since the majority of stars are red dwarfs where planets in the habitable zones would be tidally locked, which may be inconsistent with being habitable, giant moons orbiting giant planets in the habitable zones might be habitable, since they would be tidally locked to their planets instead of to their stars.
Heller and Barnes discuss whether such exomoons would be tidally locked to their planets or to their stars in "Exomoon habitability constrained by illumination and tidal heating", 2013.
On page three they write:
Point (i.), in fact, turns out as an advantage for Earth-sized satellites of giant planets over terrestrial planets in terms of
habitability, by the following reasoning: Application of tidal theories shows that the rotation of extrasolar planets in the IHZ
around low-mass stars will be synchronized on timescales ≪1Gyr (Dole 1964; Goldreich 1966; Kasting et al. 1993). This
means one hemisphere of the planet will permanently face the star, while the other hemisphere will freeze in eternal
darkness. Such planets might still be habitable (Joshi et al. 1997), but extreme weather conditions would strongly constrain
the extent of habitable regions on the planetary surface (Heath & Doyle 2004; Spiegel et al. 2008; Heng & Vogt 2011;
Edson et al. 2011; Wordsworth et al. 2011). However, considering an Earth-mass exomoon around a Jupiter-like host planet,
within a few million years at most the satellite should be tidally locked to the planet – rather than to the star (Porter &
Grundy 2011). This configuration would not only prevent a primordial atmosphere from evaporating on the illuminated side
or freezing out on the dark side (i.) but might also sustain its internal dynamo (iii.). The synchronized rotation periods of
putative Earth-mass exomoons around giant planets could be in the same range as the orbital periods of the Galilean moons
around Jupiter (1.7d$16.7d) and as Titan’s orbital period around Saturn ("16d) (NASA/JPL planetary satellite ephemerides)4.
The longest possible length of a satellite’s day compatible with Hill stability has been shown to be about P"p/9, P"p being the
planet’s orbital period about the star (Kipping 2009a). Since the satellite’s rotation period also depends on its orbital
eccentricity around the planet and since the gravitational drag of further moons or a close host star could pump the satellite’s
eccentricity (Cassidy et al. 2009; Porter & Grundy 2011), exomoons might rotate even faster than their orbital period.
So contemporary scientists agree with Dole that giant Jupiter sized worlds would tidally lock potentially habitable moons to them instead of to their stars. So far I don't see whether they also agree with Dole's calculations that satellites smaller than their planets could also tidally lock the planets to them.
I may write more on this later.
When Dole speculated about large satellites tidally locking their planets and so preventing the planets being tidally locked to their stars, our solar sysstm was the only one know. It includes terrestrial type planets close to the Sun, and giant planets far from the Sun where it is much too cold for liquid water using life.
And it was assumed that most solar systems would be like that, with the giant planets far from the stars where it was much too cold for our type of life. nobody in those days imagined that giant planets could get as to thier stars and as hot as Mars, or Earth, or Venus, or Mercury.
So Dole discusssed the possibilty that large satellites could prevent their planets from becoming tidally locked, and only briefly mentioned the possility of a habitable world being a giant satellite of a giant planet.
But when extrasolar exoplanets began to be discovered, the methods used made it much easier to detect very massive planets, and they made it much easier to detect planets that were very close to there stars. So guess what type of planet was very comommonly discovered in the early days? Giant planets very close to their stars, giant planets that were very, very hot.
So astonomers knew that if giant planets could orbit far from their stars and be far too cold for our type of life, as in our solar system, and if giant planets could also orbit very close their stars and be far too hot for our type of life, it was very propbable that some giant planets would orbit their stars at the right distances to have the right temperorures for life on their large moons.
So Heller and Barnes and the articles they cited naturally discussed the possiblity of worlds being prevented from being tidally locked to their stars by the tidal forces of giant planets that those world orbited, and which in turned orbited in the habitable zones of their stars.
And in recent years many more exoplanets have been discovered, and a wide varity of solar system types are known.
So today we know there are Earth size planets orbiting in the habitable zones of spectra l type G stars. Those Earth sized planets are far enough from their stars they don't need any giant moons to keep them from being tidally locked to their stars.
And today we know there are Earth size planets orbiting within the habitable zones of dim class K and class M type stars. These planets do need hypothetical large satellites (or possibly tidal interactions with other planets in the system) to keep them from being tidally locked to their stars.
And today we know there are giant size planets orbiting within the habitable zones of dim class K and class M type stars. Hypothetical moons of those planets would be tidally looked to their stars, except that the stronger tidal forces form the planets they orbit keep them tidally locked to their planets instead of to their stars.
What we don't know yet is whether any known exoplanets have any exomoons. There are a few candidates for exomoons, but as far as I no nobody has ever proved they have detected an exomoon yet. With more advanced techniques exommons may be discovered and confirmed.
Then we may know whether any Earth sized planets in the habitable zones of dim stars have large exomoons to potentially keep them from becoming tidally tocked to their stars. And we may know if any giant planets in the habitable zones of dim stars have large and potentially habitable exomoons orbiting them.
It has been claimed that an otherwise suitable planet would need to have a large moon to be habitable. That is a rather controversial opinion at present.
So if a large moon is necessary for an Earthline planet to support life, an Earthlike planet in the habitable zone would need a large moon to be habitable anyway, and the even larger moon needed to prevent the planet from becoming tidally locked would not be that much of a difference. It would reduced the precentage of Earth sized planets in the habitable zones of red dwarf stars, but not much more than the requirement for smaller but still very large moons would already reduce it.