A reader writes:
I'm a licensed attorney and just finished an internship at the EEOC, the federal agency that enforces Title VII (which covers sexual harassment). There are two types of harassment: quid pro quo (ie "sleep with me or you're fired") and hostile environment (defined as repeated, unwanted comments and/or behavior that is so pervasive it "changes the terms or conditions of employment")
If it's true that Cain invited the woman to his place, it's most likely a quid pro quo charge.
It's possible that the woman felt that if she did not comply she could suffer professionally – the basis of her quid pro quo charge, not that later the workplace became uncomfortable after the encounter. While hostile environment claims require that the offensive conduct to be repeated (one incident is not enough) and over a period of time, a single incident of quid pro quo is a violation of Title VII. It doesn't matter if Cain actually implied that she would suffer if she refused, just whether a "reasonable person" would conclude that she would (that's why it's never a good idea to dip your pen in company ink – pardon the phrase).
Still, you are correct; this is much, much worse than a consensual affair (worse than Clinton, whom I have no love for, as his shenanigans with Lewinsky were dumb but at least consensual). By definition, sexual harassment is objectively offensive and non-consensual. Nothing has pissed me off more during this scandal than to read conservative commentators state that sexual harassment claims are a sham that springs from otherwise innocent behavior.
Another notes:
It is not correct to say the accuser is subject to a "gag-order". That implies she is under a court order. Instead, she is subject to a voluntary "non-disclosure agreement"; if she breaks the agreement and speaks, there are civil consequences (like paying back the money), but none of them involve a violation of a court order.