With species like squirrels that are more remotely related to us, there is more scope for an argument of parallel evolution, sure. Maybe their similar behaviour developed independently and has a different cause especially when other mammals do not exhibit this behaviour.
With our much closer relatives such as apes though that exhibit so many more behaviours that are very close to ours it’s much less plausible. If all of them exhibit a common pattern of social behaviour with ourselves, arguing all of them could have independently developed this behaviour separately from us and each other, to appear indistinguishable, that seems highly implausible.
Even with squirrels though, as mammals they exhibit many behaviours common to all mammals. Behaviours we exhibit as well. So if all mammals have these behaviours and we do too, if our behaviour has a different cause, at some point our ancestors must have switched from exhibiting the behaviour due to the common mamalian cause to exhibiting it due to this new cause unique to us. I don’t find that account very plausible either.
Did our ancestors stop exhibiting this behaviour first, then develop new neurological mechanisms that happened to replace the lost behaviours? When did that happen, before or after we diverged from other apes? Maybe they have these behaviour for the same reason as us but other mammals don’t? Did we develop a parallel mechanism and the behaviour transitioned to the new causal mechanism? I’d expect to see some residual evidence in our neurology or behavioural patterns of that having happened.
>Even with squirrels though, as mammals they exhibit many behaviours common to all mammals. Behaviours we exhibit as well. So if all mammals have these behaviours and we do too...
Here you are combining speculation with an argument from the general to the specific. There are some behaviors common to all mammals, but are there any theory-of-mind-like behaviors in that category? No, so the rest of that paragraph and the one following are built on a false premise.
I am no expert, but FWIW, I happen to think that apes, or at least chimpanzees and orangutans, do have a nascent theory of mind, and that it was more developed in the various hominins that are now extinct.
Having said that, one can still consider when, where, how and how often it evolved. For example, there are many species that cache food. Some (some squirrels and also scrub jays, for example) will either only pretend to cache the food they are carrying, or move it later, if they notice they are being observed. Is that an application of a general theory of mind at work, or an instinct that evolved for one particular circumstance? As far as the ethical treatment of animals is concerned, I have no objection to assuming the former, but if we want a scientific understanding of what is really going on, that assumption cannot be made without further evidence.
What you are overlooking, I think, is that there are several possible explanations for the externally-observable behavior, and once you recognize that, there should be no paradox. In our case, we, as privileged observers of our own minds, can see our theory of mind at work, and, through language, we can talk to other people and ask how it seems to them. Neither of these lines of inquiry are an option when it comes to studying other species.
There is an interesting parallel in ethics: some people are well-behaved because they are fearful of punishment or ostracism, while some do so out of respect for other people. You can't always tell motive from actions alone.