Not to get all pedantic, but the dictionary says that "any domesticated or tamed animal that is kept as a companion and cared for affectionately" is considered a pet, and I think that is pretty good definition that might work for this site, with caveats for feral animals and the like that become pets in a companion and care sense.
These birds are neat, certainly, but since you only feed them, and then only occasionally, and don't see to any of their other care, I think they are pets in only a tangential joking way, and I don't feel like questions of this type really match the tone and intent of this site. It is entirely possible the community won't agree, but I feel like this is a good way to determine what animals to ask about.
There will always be exceptions, such as the magpies that Skippy mentions, but I think that also considering the level of personal interaction with the animal is another consideration.