Teflon does not release these fumes until it reaches almost 600°.
Any cooking oil, lard or shortning will have reached it's smoke point at a much lower temperature and the smoke produced will have killed your birds and left you coughing and the house full of smoke for hours.
Most of my recent nonstick cookware purchases have come with warnings about not using them at high heat.
So if you're going to be alarmed if teflon releases fumes, when severly overheated, that could harm any small birds that have been placed too close to the stove and could cause mild flu like symptoms that may last a few days in humans, then you should also consider not using or cooking anything that will smoke, scourch or burn during the cooking process.
I'm just saying.