I saw that story yesterday in the Guardian, and Ms Dolezal does come across as mildly delusional. The idea of "I wanna be black" is not unfamiliar -.people have staked the wish to belong and mix with black American popular culture - soul, r'n'b, tough guys and danger - ever since Lou Reed (or Bowie's Young Americans album), it's become a familiar thing with some white-skinned hiphop and soul fans, but very few of those folks have actually tried to "transition to black" irl, even short term. It wouldn't really be accepted these days.
And I think there's a definite difference between saying "I am female in my mind and in my self, even if my body (currently) has some male outward characters, therefore I want to be spoken to as a woman, identify as a woman, behave and be treated as a woman, for better and for worse - and I want to share with women's conversation about their lives and conditions" and saying on the other hand "I want to belong with the black race, define myself as one of them and share in their lives, even though I haven't lived as a black, have not been subjected to the kind of prejudice, sneer and "all-in-one viewing" that blacks sometimes (often) have to take for granted, and I want to take a front seat in speaking for my black brothers and sisters". "Being a woman on the inside" translates into many different things one can actually feel, act, do and experience spontaneously no matter what is between one's thighs, while "being really black on the inside" doesn't have much meaning IMO if that person hasn't been raised and lived as ethnically/genetically black, hasn't been subjected to some typically "black" life pressures and images but has been shielded from them, hasn't faced those social conditions or seen them nearby ("it could have been you and your kin") and then had it connected to their own dark skin colour.
Unless you'd suppose that "there is a special black mind", specially inborn black ways of thinking and feeling (or sexual behaviour?) that are essential parts of being black, and that those habits, feelings and thoughts define you as black irrespective of where and how you are living, and whether you actually are a dark-skinned person. Now that idea would border on racism, or at least some serious race/mind essentialism, wouldn't it? And if a black mental make-up, "black ideas" was something you could only have through your blood, then how could it be accessible to any non-black at all by defining themselves as black?