Honestly you are a very brave man and im glad it worked out for you and while i have never had anything like that happen to me but a friend of a friend did, his girlfriend said something similar while they were arguing and even through he dumped her and stayed away from her apparently he was so worried she might just decide to say it one day(out of spite or by accident in conversation) he left his friends and family and moved away.
With that kind of thing even a rumour can destroy your life so for me there is no explanation for why she acted that way that would make me forgive her and even if there was i couldn't trust her not to panic again so either way i would never be around her.
This is definitely a scene where you have to remove yourself from the situation and look at it from the perspective of the main character. Her rape accusation actually means very little to him. He is not in any danger. There's no police around, there's nobody around that's going to pose a threat to him if she goes through with her threat.
Worst case scenario is she goes and tells her mom, and the family avoids him. He's angry, for sure, because he doesn't want to lose the little interaction he has, but he's not in any danger. His life will not be ruined. He'll go back to how he was before.
And I think that is the major difference. For you and me, we can lose our jobs, our families, our loved ones, our freedom. That makes the threat very scary and very serious.
For MC, he would lose having someone to talk to for a few days and homecooked meals.