Yes, worldrimroamr, you are correct. But what we are talking about is the way it would be viewed by an Earth bound observer, who is in a non-inertial reference frame. I hope I get it right this time. :)
A1 = G * M2 / r2
acceleration of M1 toward M2
A2 = G * M1 / r2
acceleration of M2 toward M1
A = A1 - A2 = G * (M1 + M2) / r2
relative acceleration between M1 and M2
If you were located on M1 and you measured the acceleration of M2 toward you, then A is what you would measure, not A2. And if you were located on M2 and you measured the acceleration of M1 toward you, then A is also what you would measure, not A1. So the "relative" acceleration of an object in Earth free-fall is not independent of the objects mass "as measured by an Earth bound observer".