It isn't true that elliptical (or early-type) galaxies are metal-poor. This sounds like a pop-sci myth being propagated. The first line of the abstract of Pipino & Matteucci (2006) states that "Elliptical galaxies probably host the most metal rich stellar populations in the Universe". Thus your suspicion of the idea that "ellipticals are metal-poor" is well-founded.
Measurements of galaxy metallicities and metallicity gradients have been around for decades and show that ellipticals obey fairly simple scaling relationships between mass, luminosity, velocity dispersion and metallicity.
In terms of metallicity, massive ellipticals with bigger velocity dispersions are a bit more metal-rich than the Sun, whilst smaller galaxies may get down half the solar metallicity. The range is much larger for spiral galaxies. In addition, there is a tendency for ellipticals that are older to have higher metallicities. Examples of these trends can be seen in Graves & Faber (2010) and Li et al. (2018).
The central plot here (taken from Graves & Faber 2010) shows how the metallicity of galaxies varies with their stellar velocity dispersion (an indicator of their mass). [Z/H] is a logarithmic base 10 scale where 0.0 means the metallicity of the Sun and -1 would a tenth the metallicity of the Sun. You can see that the elliptical galaxies (red) have a relatively narrow range of metallicities, that most are as metal-rich as the Sun, that less massive ellipticals have lower metallicity and that spirals (blue) have a much bigger range of metallicity.
The reasons behind these trends are still debated. But as you rightly point out, ellipticals likely form from mergers of objects that have already been actively forming stars. A low metallicity is therefore not necessarily expected. Much depends on how much enriched gas from the ejecta of previous (higher mass) stellar populations is retained within the galaxy. Higher mass galaxies with deeper gravitational potentials are able to retain more of that enriched gas.