> In the US, you'd have to prove that they are lying which is obviously impossible.
It doesn't sound like you understand US law very well.
Proving that someone is lying is not impossible.
Holding an entity liable for defamation is also not impossible accordingly. See: the recent Virginia case, which Rolling Stone magazine lost by jury verdict. [1]
You can sue someone in the US for defamation at any time you like. During the process, you can show the lack of evidence on the other side, and you can show the evidence to support your case. In a culture that strongly favors free speech, there should be a high burden to criminalization of opinion.
If someone claims you sexually assaulted them on June 24th at 8pm, at Some Restaurant - and you can demonstrate you were never there, you're very likely to win that in court. In the US, the consequences of losing such a defamation case, are typically very punishing, which helps to limit any kind of actual free-for-all of false accusations.
[1] https://www.nytimes.com/2016/11/05/business/media/rolling-st...