While that's personally appealing to me, I worry that we tend to understand what we want to understand - there's a reason we use the expression "if a were a horse" as a parody of empathy. Though of course that's even more true of trying to make sense of other human beings, which I don't think is impossible (just hard).

I think it is very similar to human beings, except relying even more on the non-verbal.

If you have doubts about interpretation vs "facts", then I can only guess/assume that you have not had this experience.

The best advice I can give for establishing a relationship is to think hard about what the animal wants most, and try to offer it in a way that it can understand is connected with you.