I do hear the phrase “only in america” as a joke from time to time. Things that seem out of the ordinary or bizarre can and do happen in the US.
In a scenario where a woman rapes a man and has a kid, does the man have to pay child support? Yes, and here is a relevant article:
http://www.tampabay.com/news/courts/article1183449.ece
In a hypothetical scenario, judges say yes for the benefit of the kid. I think people would say that thing would only happen in America because it may not seem like it would happen anywhere else. And US judges may make decisions that provoke controversy or question.
Another example would be if a person sued another for something obscure or small. I have heard of the stereotype that claims Americans like to sue each other. I do not think it is true, but I have read about cases in the US about things that do feel too small to warrant a case. I think people would respond or think ‘only in america’ to them.