Mimicing is not producing music, plain and simple. As regards natural animal calls, that is a language all their own. Whether you can call it music is nebulous at best, as a theory, given that human beings created the concept and definition of 'music'. It makes no difference what influenced it, we are the producers of the art form, not the animals. I would like to see a parrot that knows anything about publishing rights.
The thing about animals is that while they may be able to mimic other animals sounds, they do not have the capacity to integrate it the art form we humans consider music, except maybe metaphorically. It is anthropocentric, because we made the rules.
However, this really is a digression from the question of whether or not music is a language. I believe it is. Whatever the birds believe is their business, and we'll probably never know. Their mimicry could indeed be classified as 'music' to them, and the fact that they inspire humans to make 'music' is a brief look into what they might be doing, on instinct, not on a plan. Just some ramblings for thought.