This is a valid and natural question to ask (the question is begged) and one that we wouldn't be able to answer definitively prior to genetic testing of the sex chromosomes.
Although I don't know 100% certain how this scenario you described comes out when tested, I'm pretty certain this is right; If one has male plumbing (regardless of also having female plumbing), then that's not going to happen unless said individual has a "y" chromosome (on the 23rd pair). The penis develops from the ****oris due to the "y" chromosome exhibiting its influence. In the absence of the y chromosome, the ****oris remains atrophied. Of course the presence of the y chromosome effects certain chemical levels in the body, most notably more testosterone than a female would have.
As defined by genetics, if one has a y chromosome, they are male.
Ever heard of klinefelter's disease? This is a situation where an individual has 2 x's and 1 y chromosome. These individuals usually have female plumbing but quite often have the strength of a male and other tell-tell signs (such as a strong jaw/high cheekbones). So often, a lot of these showed up in competitive sports and the Olympics. I know in the past, all athletes were genetically tested, and if a "female" came up with Klinefelter's, "she" was disqualified because well, to be quite blunt, .... males can't compete in female competition. Being males, these XXY's with female plumbing are always sterile.
Being a tennis fan, I'm highly suspicious that Amelie Mauresmo is a Klinefelters. I was suspicious of this long before she recently announced she's a Lesbian. I think she's actually a heterosexual male like all males naturally are.
The studies Ive see certainly show a strong genetic component for gender specification. They've done tons of "controlled" experiments on babies and toddlers where "gender" preferences were exhibited.
So I think the only way to counter what should come naturally is to have a warped environment. The only other explanation I'm currently open to on the matter (other than just "perverted" indulgence) is to simply categorize it as a mental disorder that should be in the DSM. I don't say that to be mean or hateful towards these people, rather I'm just being matter-of-fact about it.
We're humans and we're really, really intelligent. One can "do" anything they damn well please including, but not limited to, having sex with your same gender. Nevertheless, I say "You are what you do" only in a figurative sense.