You clarified it quite well and, assuming those raising objections weren't just picking nits, that's precisely what my earlier post meant.
One is what one's birth gear says one is, and all the surgery and/or crossdressing in the world won't change that.
I could dye my skin black and wear my caps sideways, but underneath I'd still be a medium sized white boy who hates rap and can't play basketball worth a damn ;-)