While its true that China is ahead of the game, I think there are several reasons why the US wont permit our F-16s to fly with the PLAAF flankers. Apart from the obvious and some very valid points which have been stated above, Taiwan, arguably China's biggest rival, operates several squadrons of F-16's and I think there might even be pressure from that side as well.
I doubt the Taiwanese can necessarily sway the opinions of the US government, however, if Taiwan feels that the PLAAF has ample experience in dealing with the F-16, then they will not be purchasing more any time soon from the US. And obviously, US wants to lock up as many contracts around the world.. especially in this very competitive, high-stakes, multi-billion dollar field.