I doubt that's accurate, I was always under the impression that AAMs are "salvage-fuzed" firstly to minimize collateral damage on the ground and secondly to deny intelligence to the enemy. There is a very famous precedent for the latter, the Soviet AA-2 Atoll as a copy of the Sidewinder owes a lot to an unexploded missile brought home in its tail pipe by a MiG-15 during the Korean War.
Korean War ended in 53, sidewinder did not enter service until 56.
The incident you are referring to was a clash between PRC and ROC pilots in the Taiwan Strait.
However, I would be extremely surprised if missiles don’t have some sort of self-destruct. It is simple enough to implement, and not doing so would leave unacceptable risk of hostile forces recovering largely intact missiles.
For most if not all confirmed AMRAAM kills, multiple missiles were fired over hostile territory to achieve those kills.
If there wasn’t a self destruct, then you would have thought the Serbs, Iraqis and others might have found at least one relatively intact missile between them.