If there were other wreckage inside Pakistan from that encounter then it'll eventually come out. Maybe not right away. Not even ISI can completely prevent leaks in the age of internet connectivity.
You are right in theory, but remember the Taliban knocked out 3 AEW&C in PAF service. Blew up one, damaged two. Did it come out? No.. it finally "leaked" because of a Pakistani politician asking for funds in Parliament and some Swedish paper mentioning the extra business coming Swedens way.
In Kargil, India literally shamed Pakistan into taking 8 regular Pakistani soldiers back.. they were unclaimed & a secret PAF jet came to pick them up after India threatened it would start releasing recordings of those men to the WW media.
Pakistan is NOT a normal country. The PAF is integral to the average Pakistani's myth making about his invincible country & the loss of a F-16 to a MiG-21 will not be taken well.
In this milieu, the ISI will do all it can and has already, to prevent this news from leaking.
India can shame Pakistan by having WingCo Varthaman repeat his briefing to the wider public, share AWACS tapes etc. This has two problems. One, the ISI will just execute any captured IAF pilot in the future. The IAF is an offensive AF & the likelihood of more of its crew being lost over Pakistan is high. FYI for those who don't track these topics.. many families still believe their family members are held by Pakistan as a sort of of tortured punishment for the 71 ops. Many accounts of these. The Govt of India hasn't been able to and nor has it been interested in doing more than just giving demarches to Pakistan.
Second, releasing AWACS footage gives away classified capabilities. The resolution of the AWACS against these targets, the data captured etc. All this stuff is real gold to any opponent force.
Net, Pakistan will continue to deny its way through the whole topic. But please check the past history of the two states to get a clear idea.