Children having sexual urges towards and crushes on adults is pretty normal–particularly once they hit early pubescence and are flooded with hormones–so I don’t necessarily see it as a sign that a child has already been abused. But, again, an adult acting sexual towards any child is absolutely, 1000% wrong.
The perspective I’m coming at this from is that, based on feedback I’ve gotten over the years, I was sexually precocious, and my parents responded by, first, shaming, and second, taking me to a professional because they were sure something was “wrong” with me, and that it needed to be “fixed”. That ended up being deeply harmful to me, and it’s taken me decades to reach some kind of detente with who I am. (The psychologist was actually quite supportive of me. He said my parents were wrong, and that I was going through normal things, albeit at an earlier age than most. But that didn’t really help with the load of shaming that I was getting from my parents and religious leaders.) Parents freaking out and immediately going to an authority is going to have that kind of effect on a child. IMO, it would likely be better for parents to have a very frank, but non-judgmental discussion with a child before leaping to the conclusion that they were acting out because they were abused, rather than because they had a colossal lapse in judgment.