It's regrettably understandable. Even if you trust your HR department and the courts to eventually unravel and diffuse a false accusation, can you say the same thing about social media? How will you hold them account for spreading a false rumor? Sue all facebook users? Zuckerburg? All you'd need to do is to make a convincing enough post with plenty of emotion about being harassed, and then sit back. Morons these days click "share" before they even read posts.
"Don't be an asshole" is disingenuous. Obviously don't be a asshole, but realize that even if you're perfectly well-behaved, some one could accuse you and possibly get away with it. More likely, an awkward misunderstanding could spiral out of control. Personally I believe people are unrealistically unforgiving of people making mistakes nowadays, but that's a different discussion for another time.