Yes. I think that what she actually meant by that is that she considers her gender to be biologically determined as opposed to a "desire" or the result of some environmental factor.
The issue with that statement is not the position stated above, assuming I interpret her correctly, but that the statement violated what had been previously (mostly) agreed to terminology for the discussion: male/female referred to sex, man/woman referred to gender. She wished to claim both terms to refer to gender. Or perhaps its more accurate to say she did not want her sex referred to.
Further, and I may be mis-remembering this, I think she also considered her sex to be female. But I think that for her, gender overruled sex to the point that sex did not matter to her. Anyway, for whatever reason, she found being referred to as male to be offensive even when the reference was to her physical sex, not her gender.
This conversation is largely about sex and gender as separate (but linked) concepts. That separation of terminology is necessary. Unfortunately, when discussing the condition and experiences of a person participating in the conversation, it may be triggering because those same types of statements in other contexts have been weaponized.