Thanissaro Bhikkhu's talk on this issue is good, from a Theravada perspective. Title is "What is Wrong with Buddha Nature"http://www.audiodharma.org/talks/ThanissaroBhikkhu.html
I'd say that the concept itself isn't "wrong," though it's not a part of the Canon, therefore we would say it wasn't taught by the Buddha. But even the concept itself has a few different dimensions. If you just think of it as Nibanna then there's no problem. If it's simply the innate capacity to awaken, I think we all have that potential - but maybe it's going to take you a lifetime and me an Aeon or two (thousand...billion).
If you say we all are already awakened, of course that's a problem, because you can't be awakened and still have the kilesas (defilements). So that doesn't work from a Theravada POV.
Calling it a true self or any other kind of self is a problem because the Buddha advised against pretty much any form of self identification you can come up with - even grand noble ones like a cosmic self, true self, one with the universe, etc.
Mahayana has ways of addressing these issues with it's own kind of logic, but they just don't work in Theravada. The Theravada ideal is arahantship, and not Buddhadhood. Since a Buddha is self awakened, a Buddha can't be a person who is currently studying the teachings of the Buddha of the current period, so none of us can be Buddhas as long as we are studying the teachings of the Buddha!