I think that's because the narrow scientific term domestication is used in casual speach with a shifted meaning. And that's because we don't have any other expression for animals that you can be friends with that would sound as cool as domesticated (taming is too tame).

Edit: Sorry, got lost in the threads. I'll leave it here because it is still kind of on topic. I guess I should also add that domestication is a process and the line where an animal is considered domesticated is arbitrary.