I do know of a sister that claimed rape and wasn't raped. She was young and got pregnant, then cried rape. The elders told basically all of the family heads what was up so that nobody was stumbled or wondered what was up when she started showing. I was a ministerial servant then, I think.
Anyway, turns out she had been dating a Mexican guy on the down low, and her claims of being raped by a Mexican man ended up with her married to the guy down the line, trying to help him get legal, working with my mom cleaning houses, my sister baby sat for her, etc. She and her husband seem to have a good marriage. I mention the fact that he's a Mexican because in the area I lived then there was a paranoia about these Mexicans that didn't speak English and were kind of mysterious to the good ol boys. So there was a bit of a built in narrative already.
You can see why someone might claim rape in such a situation. So much is at stake, and being pregnant she probably just went that route not knowing where the relationship was going but knowing that she'd lose all relationships if she was disfellowshipped while pregnant. She did end up disfellowshipped. I do believe it was for the duration of her pregnancy and beyond. It was quite the scandal.
Ultimately those men shouldn't be handling cases of criminal activity like rape anyway, but you can't just take claims of rape at face value, which is why there are professionals trained in that way (to actually help legit victims, which elders don't do anyway, and to investigate whether or not there's enough to bring charges on such a matter). Unfortunately such claims are made falsely at times and innocent people's lives are ruined. It's way beyond the pay grade of an elder.