You could also look at it from the other way round. If an F-16 was indeed downed by Mig21 then that's a huge embarrasment for PAF and also for the Americans who want to sell F-16s to India.
On top of that, there's a clause in agreement of F-16 with Pakistan that they can only be used against terrorism. IAF already showed the indisputable proof with the AMRAAM pieces that F-16 was indeed used in this operation. PAF is trying to come up with a version that can please both their internal audience and the Americans.
Even with very old tech you kind of underestimate India. We're more than capable of performing such operations. I mean if we were able to do in 1971 why wouldn't we be able to do it in 2019 when we have over 300 Sukhois now?