Is it possible that these deep concepts are pointing to the same thing at the end of the day?
Yes I think so.
Part of Buddhist doctrine is, more-less, that self-views are a cause of suffering.
I get the (not very well-informed) impression that the Hindu tradition includes teaching something like, neti neti -- "the self is not this".
A corollary of that search might be that the "self" or Self is something other -- is Atman or Brahman.
Perhaps a Hindu would expect a Buddhist to somehow identify with Nibbana (or the Tathagata), see that as some refuge for a sense of self (or of being, or of action, etc.).
So if selfishness and identifying with the body and the shandhas is an extreme (worldly) position, maybe Atman and so on is logically opposed to that -- and a different extreme!
Whereas Buddhism being a middle way, neither extreme, might say, "not the other extreme either -- i.e. also nibbana isn't self, is anatta".
Wikipedia's Paramatman suggests that the (or some) Hindu doctrine might be similar somehow ...
Selflessness is the attribute of Paramatman, where all personality/individuality vanishes.
... but that article's comparison with Buddhist doctrine says only ...
Buddhism rejects a metaphysics of "ground" such as the paramatman.
I think that there is some Buddhist "metaphysics", and sometimes some doctrine about "ground" (but those are a couple of words I don't know enough of at the moment to explain).