Does Jake the Crow believe he is a rabbit because he is living with them?

Jake and his rabbit buddies. Screenshot.

The news media say that Jake the Crow believes that he is a rabbit because when rescued with a broken leg on a road he was placed with rabbits in a rabbit hutch and he gradually got used to them and now spends all his time with his rabbit friends. The people who rescued him say that he thinks he's a rabbit because he hops around them and does things with the rabbits.

But a quick bit of research tells me that this is unlikely to be true. Yes, he likes to live with the rabbits because he has learnt to trust and accept them and vice versa. That's a great thing and it is a good example of an interspecies relationship

However, it's a known fact apparently that crows are self-aware which means that they can recognise themselves in a mirror. They know what they look like. They understand what and who they are. 

And knowing what they are i.e. a crow, when they look at a rabbit, they must understand that they are not the same creature. They must understand that they are looking at an animal that is different to them. Therefore, they can't think that they are rabbit.

A minor philosophical point I guess but I believe one that is worth making. His rescuer said that:

"The rabbits have accepted Jake as one of their own. It's so funny, he hops around them and Jake has taken on the characteristics of the rabbits, and we know when he wants feeding because she lets out a big squawk, which is also why we call him Jake the Really Loud Crow."

Yep, he has copied some rabbit characteristics but he still knows that he is living with a different animal.