At this point, it would probably be the better idea to wait for a practitioner to join in and answer, or at least someone that actually has some vague idea of what they're talking about and isn't just making WAGs in regards to the hindu perspective.
My own WAG would probably be that intelligence actually has a lot to do with it. You have to be able to understand the illusion to step beyond it and whatnot, or at least be aware of your own lack of awareness. And beyond that, most of the greater expressions of the brahman (i.e. the gods) are largely human in shape. It's reasonable enough to assume that those things which are closest to the greater manifestations known are higher truths. Doesn't preclude the possibility of higher entities above the known gods that are animal-shaped and whatnot, nor does it preclude the possibility that our own perception of the truth has colored our perception of the higher entities, but the brahman doesn't really preclude much of anything, technically, so far as I know.
Really, when it comes right down to it, humans are the only species I'm aware of that can actually dance. There's plenty of mating and territorial displays out there, but to dance just to dance... that's pretty much ours and ours alone. If anything puts us closer to the hindu conceptualization of the gods, it's probably that.