Happens so rarely it is pretty much a non-issue.
It's happened to me so this is definitely not a non-issue for me. I had someone harass me online making all sorts of accusations of "crimes" I've committed and threatening to report me to the police. She claims god talks to her - so no use arguing with her. Do I actually think the police would do anything based on "Hi I'm RANDOM PERSON and god told me this guy's evil?" Of course not. She could make my life a living hell, though if she knew my real name and address. (She was harassing me on a site where I use a pseudonym.)
In case you think she couldn't do this, she was harassing someone else (one of many people she's targeted) and knew his real name and place of employment. She called his job (he's a teacher) and claimed he is a pedophile (a serious accusation in any case, but needless to say, a career killer if you're a teacher). Luckily, he notified his employer beforehand of her and they brushed her off. She also used Facebook to track down all of his relatives (and people with similar last names) and tell all of them that he's a criminal.
Luckily, this person isn't the "travel to your home and take matters into her own hands" type, but who knows when she might get frustrated that the police aren't following up on her "god told me" claims? At one point, she might decide that showing up at my front door is god's will. I definitely wouldn't want to be broadcasting my home address to her and every other sicko online.