The key is in "as seen from Earth". Mars is illuminated by the Sun and the distance from the Sun varies only slightly. Therefore, it is always the same brightness. A photo of Mars through a telescope will always use the same exposure no matter how far it is from Earth. The planets do not behave like point sources of light. When Mars is twice as close, it fills 4 times the area in the sky. This exactly counters the inverse square spreading of the light from Mars. The same is true for all the planets. If they got brighter as they get closer, they would get brighter as YOU got closer. The Apollo astronauts would have boiled then vaporized as they approached the Moon. It is a common error. N. D. Tyson makes it with a truly dumb statement near the beginning of his Cosmos series. Something about the brightness of the Moon long ago when it was closer to the Earth. Think of how many people read that script and it still slipped by.
The brightness of an extended object as viewed, is not the same as the illumination it provides. If the Moon filled the sky, it would not look brighter. You would not have to wear welder's goggles to look at it. But the total amount of light reflected on the Earth would be much greater and more like the illumination on an overcast day (and there would never be a full Moon because the Earth would get in the way).
You can easily calculate a brightness compared to the Earth (or Moon) daylight brightness and the ratio of the squares of the distance from the Sun.
When you add that you want brightness as perceived from Earth, it depends on distance and phase. If you think of it as wanting to read by Mars light, it is "brighter" if it is closer and it is "brightest" at "full Mars" or opposition.
There is a gaggle of terms used in optics to describe various ways of describing brightness and intensity and illumination and they get very confusing.