I was with you until you equated race with non-physical traits. Non-physical traits are cultural and societal. While these cultural and societal aspects may be more present or dominate a greater portion of a race, people are not born with these. This is why prejudice and stereotyping based on your physical appearance is so silly.
The term race has morphed into meaning more today than it has in the past. "Trans-racial" is ill-defined, and quite frankly, inaccurate, useless slang. While I completely agree that Dolezal's actions were unsavory, I think (another made up, slang term, but IMHO more accurate) what she was trying to impart is she feels she is "trans-cultural" or "trans-social". Of course these are just additional slang words that are nearly useless too because in today's world, especially if you're an American or part of some other nation (or even on the internet unresticted), that more often than not, welcomes rather than suppresses people of all backgrounds, we're all "trans-cultural" and "trans-societal" to some extent. The old term (which I think is still perfectly acceptable) is "cross- cultural."