If you take a look at article 130 or New York penal law (only using NY because that's where Columbia is and where this whole thing went down) the language for rape specifically says 'he or she engages in sexual intercourse' (in any of the degrees) and sexual intercourse is defined as "ordinary meaning and occurs upon any penetration, however slight". Because the language says 'he or she engages in' that leaves the possibility that both men and women can be charged. No, a woman cannot penetrate, however she can engage in sexual intercourse. Not hard to understand...
I don't believe that stigma exists at all. Men are applauded if they are successful, rich and powerful, but they are also applauded if they go become reclusive mountain men. Look at skiing. Yes, there are a few high paid skiers, but some of the most respected live out of vans and deliver pizza. Men can do pretty much whatever they want (be successful or not) without too many repercussions.
As for the rape thing? I'm willing to bet there are far more legitimate rapes on and off campus that go unreported for every illegitimate, girl-who-cried rape situation.
Also, the lines between rape and sexual assault can be pretty darn close. Again, from article 130 of New York penal law. Rape is vaginal intercourse. Criminal sexual act is oral or anal intercourse. Aggravated sexual abuse is penetration with an object. There are degrees of severity to all of these acts. It's not always a cut and dry situation, especially when drugs and alcohol have blurred what exactly happened.