Sounds good IRRenewel.
I think the clue is in this statement (my bolding):
In a 9-G turn, both planes' centrifugal force will increase ninefold. In order to maintain a 9-G turn, the lift (centripetal force) must also increase ninefold. To do this, the 160 lbs./sq. ft. wing-loaded plane must increase its angle of attack a certain amount, but the 80 lbs./sq. ft. wing-loaded plane doesn't have to increase its angle of attack as much as the first plane has to.
This isn't true is it? If the apparent weight of the aircraft doubles, then the lift must double to compensate. If the speed is the same and all the other parts of the lift equation are the same allowing us to only change the angle of attack, then the AoA must also double to achieve the extra lift. This is the same for the high wing loading and low wing loading aircraft.
The difference comes about because the high wing loading aircraft already has a higher angle of attack and as IRR says, it will reach its stalling angle sooner, but up until it stalls, it's turn rate and radius would be the same as for the other aircraft.
Reading it again, I think he is correct but isn't quite saying what you think. It seems to me that he's basically saying the low wing loading aircraft can pull more Gs than the other aircraft and can therefore out turn it, but it must pull more to do it.