Having a bird in the kitchen is just a bad idea (unless you are going to eat it). If you overheat oil, that becomes toxic as well and will kill a small bird the same as overheating teflon.
You might have a house with a kitchen next to the living room and no door in between, and if you've got everything closed up in winter you can kill a bird in a nearby room with Teflon toxicity. Overheating oil will not kill a small bird, and even some quick smoke inhalation won't necessarily kill a bird.
> Abstract: Japanese quail and parakeets were exposed to the pyrolysis products of: (1) commercial fry pans coated with Teflon® finish, (2) plastic fry pan handles, (3) corn oil, and (4) butter. Other materials used in the test were commercial aluminum fry pans and cast iron fry pans. A four-hour Approximate Lethal Temperature (ALT) was determined for each test material for each specie. All products tested were lethal to Japanese quail with ALT's ranging from 260° C for butter in cast iron to 370 °C for a plastic handle in a glass container. The ALT for a fry pan coated with Teflon® finish was 330°C. All products were also lethal to parakeets with ALT's of 260°C for both the pan coated with Teflon® finish plus butter and the cast iron pan plus butter. The ALT for a fry pan coated with Teflon® finish was 280°C.
