2018 Ig Nobel Prize in Anthropology winner: Spontaneous Cross-Species Imitation in Interaction Between Chimpanzees and Zoo Visitors [1] "[...] for collecting evidence, in a zoo, that chimpanzees imitate humans about as often, and about as well, as humans imitate chimpanzees." I think this is evidence towards your point that we understand very little of cognition of other species.

[1]: https://link.springer.com/article/10.1007/s10329-017-0624-9