In any case, it's actually more-or-less irrelevant in arguing whether a trans person is actually the gender they identify as, and is mostly a curiosity until it leads to more focused treatment. The bit that does matter is the last question - am I who I am in my head, or am I who you think I am?
No. You can think yourself into a different gender. Gender isn't sex - this has been written about since 1963, and is generally agreed on at this point - gender is a combination of personal and cultural mental attributes, while sex is generally "what your body physically is". This messes up slightly when you get to certain sex-driven gender attributes, but, in general, it's a reasonably clear line.
Sex is mostly irrelevant unless you're intending to sleep with someone or you're a doctor, and even then what you're asking about is generally a certain set of characteristics where a number of people fall between the lines. If you're a trans woman who's undergone GRS and you say "my sex is male", that's going to confuse an awful lot of people.
Edit: My specific point, in this response, is that identifying as a gender which does not match your sex is not "playing pretend" or less important somehow, as you insinuated in your original post.
Source?
If the difference is so clear in an MRI why not run a simple blinded study where researchers look at brain scans and tell you who is transgender and who is not? Such a study would not only prove this theory outright, but would likely make a researcher's career.
[0] A sex difference in the human brain and its relation to transsexuality http://faculty.bennington.edu/~sherman/sex/TRANSGENDER.pdf
[1] Male-to-Female Transsexuals Have Female Neuron Numbers in a Limbic Nucleus http://press.endocrine.org/doi/full/10.1210/jcem.85.5.6564
[2] Regional gray matter variation in male-to-female transsexualism https://www.ncbi.nlm.nih.gov/pubmed/19341803