This kind of thing happens far from New York and often doesn't involve sex at all. I live in the Southwest, and "imaginary" crimes are quite common. I would suggest their prevalence is due to a kind of arrogance of power on the part of police and prosecutors. I routinely go into court to fight crimes that aren't crimes, crimes whose elements have not been met, enforcement of laws declared unconstitutional, etc.

As one simple example, there is no law hereabouts that says a person must "immediately report" an accident unless it is "apparent there is over $500 damage." The plain language of the statute, and oodles of case law, say that in the case of a 'paint scrape' or 'fender bender' people can just exchange info and go on their way. Not according to the police --- they will ticket everyone who does this and get downright mad in the process. "You can't leave an accident without permission from the police!" they will often insist. Wrong. Yet they still write tickets, never even addressing damages. They normally just look at the title of the statute, and ignore the text.

I currently have a case where in 1994 the Federal Court declared that a provision of a state law (allowing certain arrests) was not only unconstitutional, it was so "obviously wrong" that police who followed it were not to be given "qualified immunity". Back then, when the police argued that their interpretation of the law was just, the court declared their argument "patently ingenuous". 15 years later, I am back in court pointing out this out, and the best the prosecutor can do is "well, I think we've gotten away with this many times over the years..."

On the misdemeanor end, an awful lot of these "imaginary charges" are cases of the cops playing judge and executioner. A misdemeanor committed "in the presence" of an officer is arrestable. So they arrest you, you spend hours to the weekend in jail, you have to bond out, you show up in court a couple of months later --- and much of the time the prosecutor 'declines' the case (thus it isn't on their stats) and the cop simply doesn't show up in court. Dismissed for "failure to prosecute". You won't even get an apology, let alone any compensation for being arrested, etc. (and maybe car towed, etc.).

Practically speaking, there is no remedy. The cops basically toss whomever they please in jail, making up crimes if need be. They figure by the time you've gotten the case dismissed, you have "learned your lesson." And indeed you have -- all that stuff they taught you High School government class was really just so much propaganda....