Your link is mixing up the two molecules by calling PFAS "The Teflon chemical". "Teflon", the non-stick final product, is PTFE with a very strong fluorine chemical bond and no chance of reacting with the human body at normal temperatures (That's why nothing manages to stick to it, basically). PFAS were used by DuPont in the manufacture of Teflon (and recklessly dumped into the environment).

PFAS are an ecological disaster; Teflon itself is not a concern.

Birds have fragile high performance lungs.

Using teflon cookware around a pet parrot is a well-known way to kill the pet.

Teflon frying pans are supposed to be safe if you never let them overheat, but in practice they're not safe if you have birds in the house.

PTFE is toxic for humans too, but human lungs are more robust than bird lungs.

Sure polymer fumes are bad, but this is about oiling a bike chain.

"Normal temperatures" is the key thing, "unattended frying pan temperature" is different altogether...