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 noninertial reference frame. I hope I get it right this time. :)
A1 = G * M2 / r^{2}
acceleration of M1 toward M2
A2 = G * M1 / r^{2}
acceleration of M2 toward M1
A = A1  A2 = G * (M1 + M2) / r^{2}
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 freefall is not independent of the objects mass "as measured by an Earth bound observer".
