Humans are made of both biological and memetic (social) stuff, though. It's famously difficult to ascribe any particular behavior to just one or the other -- the old nature/nurture debate being one aspect of that -- but even if you could, you can't necessarily describe one side of that as more "real" than the other side -- I am both my flesh and its neural activation patterns. One reason I believe most transgender people describe a purely physical (brain) basis is that using the language of desire is severely socially proscribed: it's not viewed as OK to merely say "I want to be a man/woman" the same way someone can say "I want to be an architect", although in both cases a person may simply be looking around at the various roles their society has on offer and finding some desirable than others.

This phenomenon isn't limited to transgender people; even 15 years ago gays and lesbians were viewed more negatively by society, and magazines would run articles about "the gay gene," despite the lack of evidence for its existence. Nowadays, in a much more tolerant culture, you can find people who say that they "choose to be gay." A similar evolution in transgender self-description could happen if society becomes more tolerant.

So, I think this is actually evidence simply that behaviors or accomplishments viewed as highly unusual (either positive or negative) are often ascribed to a physical basis, whereas anything perceived as being in the normal range of human behavior in the culture is seen simply as the individual's choice or self expression. This doesn't actually tell you anything about the cause of the action or desire -- we can't do the kind of experiments that would be necessary to find that out. For all we know, desiring to be a particular gender, or desiring to have a particular occupation are similar mixes of built-in brain organization, body chemistry, psychological imprinting, culture, and both conscious and subconscious weighing given the individual's other abilities and limitations.