She's right -- surgery doesn't change gender.
It only helps one's body conform to the gender they already are. Getting surgery doesn't turn a man into a woman (or vice versa). They were already a woman, and the surgery just helps them look and feel like it. A trans woman doesn't become a woman when she gets a surgery -- she becomes a woman when she realizes she's trans (or, rather, realizing she's trans reveals to her that she was always a woman).