My family learned this after replacing a stove with one that had a non-stick interior a couple decades ago. That was a pretty major bummer.
On top of that you have to heat the Teflon over 500F / 260C, and ovens temperatures don't go so high (except in self cleaning but a non-stick oven would not have self cleaning).
I suspect something else happened to your birds - probably simple smoke from food residue, which kills birds much easier than overheated Teflon does.
I don't know whether they're being intellectually dishonest, or genuinely don't realize they're spreading useless info.
They're claim that nobody gets a pan hot enough to degrade teflon while cooking is slightly more reasonable, except plenty of recipes start with "heat an empty, dry pan until it is searing hot" and that leaves a lot of room to screw up your pan.