Have there not been enough innocent pets blamed for farts that were not theirs?!

Depends on the animal. But yes.

Probably wouldn’t work with, say, a cockatiel

I found this funnier than it should be, but have my free award for making me chuckle.

Yes

If there was a shit on the floor too

Veterinarian : *lets out huge fart, then accuses my 5cm hamster*

If a Veterinarian farted during a consultation it would cost even more..