1) I had my question answered to my satisfaction, so I was gonna let this go, but I do have to say one thing about this whole #metoo scare stuff. Solve this inequality:
# of women raped by men _____ # of men falsely accused of rape / sexual harassment
If the answer is even a little bit unclear, consider the fact that a "successful" crime is where there are no public repercussions for the perpetrator (no gossip, no accusation, no indictment, no conviction). Now consider that while a man can commit a "successful" rape, it is impossible for a woman to commit a "successful" false accusation of rape. In other words, rape can be "costless" for a male perpetrator, but a false accusation is not "costless" for a female perpetrator. Her life will be tossed upside down as well. See, e.g., Monica Lewinsky, who I think didn't even accuse Bill of anything.
2) As to the alone time thing, depends on what you mean by alone. If "alone" means "in my office with dozens of other offices nearby", I am alone with women all the time and it bothers me not one whit. And I have a hard time believing that any "normal" man (or better) could not generally comport himself in a manner such that *no one* would believe a woman who falsely accused him of something untoward. If "alone" means "in a hotel room", well, duh, don't do that.
3) That said, I am aware that *certain* men, far richer or more important than me, can be targeted for money or whatever. I have heard that new NBA, NFL, etc players are taught, whether formally or informally, that they should beware predatory women and should, for example, take their used condoms with them when they leave a place lest the woman dig it out of the trash and try to inseminate herself with its contents. No idea if that's true, but this concern would likely apply to a very, very small percentage of the male population (compared to, for example, the 30% or so of the female population that is sexually assaulted, last I heard).
TL;DR - rape is a real problem; false accusations of rape is not.