This isn't what we are discussing though. We are discussing whether all men who claim to be women are transgender or not. If you are going to say gender is innate, then surely they are, and there is no genuine or fake transgender people because being 'trans' is predicated on self knowledge not biology. Thus, Stephen Wood and Isla Bryan are as genuinely transgender as someone with a GRC.
You need to go back to what I said in my opening post.
I can't define the term 'transgender'; neither can anybody else, since its meaning is culturally different from place to place.
At one time there were some accepted terms, example, cross-dresser, transvestite, CD, TV, T-girl, transsexual, TS etc, The term transgender was often used as 'transgendered'. These days people are avoiding the terms transvestite TV, TS, transsexual.
Look on a dozen different websites and get a dozen different answers. If there is a word that needs defining it's maybe that one.
In the meantime there is no fixed identity of transgender. But because many in the LGBT community see it as an umbrella term, there are those who will say they are transgender because they cross-dress. This is a fact and it makes reading and interpreting data sets especially difficult.