No, I believe you should not do that
Like what you said, it doesn't violate forum rulesOfcourse, but it's up to moderators to deal with the rules. The trust system is not about rules, but about trust. Is it possible to trust a user who shows personal correspondence? Would you trust someone who shares your messages without permission?
we should not publicize private messages to the community. But it does not mean that it is not allowed, in some cases,
I think you're right here. In some cases, posting private message can resolve public disputes. If the publication is not provoked by public discussion, then I consider such a publication unacceptable.