> this is something I never understood of the Law about these kind of settlements, if someone pays something to the other party, something wrong must have been done

With a civil suit, that's not necessarily the case, because there is a very different burden of proof compared to a criminal case. For civil trials the burden of proof is preponderance of the evidence, which means that the plaintiff merely needs to show that the fact in dispute is more likely than not. In comparison, criminal trials require a much higher burden of proof known as beyond a reasonable doubt.

> https://www.law.cornell.edu/wex/preponderance_of_the_evidenc...