I've never assumed that, but it's fair enough if that's what other people think. I thought it was more the case that the Ministry assumes that parents will prevent their children from using magic outside of school, and it prefers that the parents will punish their own children for using magic. Magic used in the Dursley's house was assumed to be Harry's because the Ministry assumed he was the only one in the house capable of using magic (so presumably it's a blanket detection of magic, the trace on an individual wouldn't have worked here).
I think a fifth year receiving duelling lessons is completely fine. There would be adults present so the student would be supervised. Bear in mind as well that students *can* be homeschooled, so they would be performing magic outside of a formal school in those circumstances, as well.