What proof do you need that "she" is a man? You wanna get a look at her Junk to be sure? Maybe "she" had a sex change surgery. Why would s/he have to prove it to you? Or anyone? If you didn't know that s/he had female genitalia how or why would you give a $hit what bethroom they use? Why does that change when you (think) you do know?
Sorry- seems weird to me that anyone is so obsessed with genitals.
This person looks and acts like a man to anyone that looks at them. They should use the men's room where THEY feel comfortable.