I heard that once Gonzalez got inside the White House, the Secret Service agent at the door tried to stop him but it was a small woman and he overpowered her. So political correctness could have had fatal consequences if the off-duty agent had not come along at the right moment to tackle Gonzalez.
I don't think anyone knows exactly what happened. But since we're speculating then perhaps if the door had been locked or if the Secret Service had not turned off the audio door alarm at the request of the White House Usher then the Secret Service agent might not have been surprised and overpowered. It was a comedy of errors from start to finish. I doubt the gender of the agent made things any worse, or that had it been a guy it would have been any better.