Directly speaking, you are correct. It is not reflective of reality. The interesting question is whether or not this is a reasonable solution to the mental health problem of gender dysphoria-- which is indeed real and well-documented. I have kind of wondered whether CBT or some other evidence-based therapy treatment might prove better for gender dysphoria, especially if gender dysphoria is a result of a) discrimination-related trauma (e.g., a gay man who is bullied for being feminine, a masculine woman suffering from a high degree of internalized misogyny) or b) other trauma, particularly sexual assault.

It may be that all of this-- people transitioning, experiencing gender dysphoria, etc.-- is some combination of trauma symptom expression and other forms of mental illness. The limited research evidence so far suggests this (e.g. the startlingly high rate of personality disorders among trans people-- why is it so much lower for LGB, if they are compared to us?).

But, who knows. I believe that including mental illness in the discussion is an important first step and that's why I am inclined to be sympathetic towards trans people who are bringing that to the table-- even if they still are being "inauthentic" in regards to their presentation. At least some of them are just trying to navigate the world as best they can, I think.

Just my 2 cents :)