Was Elizabeth I A Man?

Okay, this was a new one on me, the idea that Queen Elizabeth I might actually be a man.  I had actually never heard this rumor before until I watched The National Geographic Channel's special THE SECRETS OF THE VIRGIN QUEEN.  Guess what? There were no real secrets in this special, just a bunch of rehashed stuff about whether or not she and Dudley ever had a child, and why she never married.  The only new information (at least for me) was the story of the Bisley Boy.

According to THE SECRETS OF THE VIRGIN QUEEN, Elizabeth (then a princess) had died aged 10 while staying at Berkeley Castle, in  Gloucestershire (the same castle where Edward II was murdered). Her minders, terrified of the retribution of her father, Henry VIII, made a substitution. A lookalike boy from the nearby village of Bisley was put in her place and sworn to secrecy. This legend 'explained' why Elizabeth never married or had children. In fact, the tale was apparently invented as a joke by a local clergyman in the 19th century.  Bram Stoker picked it up and wrote about the story in his book about Famous Imposters.

The show contained interviews with the residents of Bisley who apparently do consider the idea that Elizabeth I was actually a dude.  One more cynical resident admitted that it was good for tourism.  They tried to pass it off by suggesting that she wore all those ruffs to hide her Adam's Apple, and that the white make-up she wore was to cover up her stubble. The one valid point that was brought up was the fact that Elizabeth I didn't want an autopsy of her body after her death. Although that could have been because she didn't want anyone cutting her up, or she wanted to conceal the fact that she wasn't actually a virgin, which is more likely.

This is my question, given the fact that Elizabeth spent her life surrounded by women who dressed her and undressed her everday, and the doctors who examined during her lifetime, how could she conceal that she was a man? I think people would have noticed that she had a penis! Especially since she did apparently get her period, if not regularly, then often enough. Plus even though Henry might have been a neglectful father, I think he would have noticed that his daughter now had an Adam's apple!

Has anyone ever heard this story before?