The US does indeed have some interest in keeping any shoot down of F-16 well hidden. They will be less inclined to market the F-21 to India if this is true because the Indian officials will know for sure if the claim is true or not.
Not as much as it used to.
First with the rising F35, F16 is not as hot a seller for big buys. The current orders are Slovakia, Bahrain and Taiwan. India was the largest potential new buyer. With Slavikia (to replace Mig21s) and Bahrain (adding to there fleet) both ordering about a dozen to two dozen. Taiwan would have been second largest and really doesn't have much of a choice in orders because of the Great wall the PRC erected to prevent FMS. Besides most of its order was refit of its current fleet. India would have been the largest new order that's why the Indian production line and F21.
Second even if it did happen come in that category of "one in a million" that moment when the sun and moon fall into perfect alignment. It's possible don't get me wrong in training exercises F22 has been "shot down by T38s. But actually in the skies...
Third Pakistani Vipers are older machines even with the second hand Jordianian machines A and B units lacking a lot of the more advanced upgrades.
Finally the US tends to be fairly open on losses. Sure there are claims of but Nation X shot down this... but then again Argentina claims to have Sunk the HMS Invincible. Claims don't make downed jets.
No tracing of the AMRAAM to Taiwan yet.
It's possible that some missiles in that Lot were sold to Taiwan. Lots are not nation specific. It's based on how Many standing orders there are or are protected to be. So that Lot for FMS might have ended up going to dozens of countries. Including Taiwan, Including Jordan including the UK or Greece or Turkey.
I can't say for absolutely certain on this but I do know that when the US first introduced the Aim 9 Sidewinder, the Russians reverse engineered it.
Stories on how very. One claim is that after the US refit Taiwanese jets during the 58 crisis, one Sidewinder dud was left stuck in the side of a Chinese fighter. Another is that a Swedish officer sold the Soviets the blueprints.
I like to think some combination of the two. Either way. The K13 Atoll missile is virtually interchangeable with early Aim9 right down to part numbers
So the ability to reverse engineer the interface between a host fighter and missile is not unheard of. Since Pakistan was the customer they may have granted the PRC access to there inventory, Or done it themselves.
Either way the missile I take as confirmed the launch platform yet to be determined absolutely. I side with a JF17 though. That said because of the ranges involved and locations said it seems like an F16 could have fired an AMRAAM and still remained in Pakistan well taking down a target.