> In any case, I would never charge a summer student. And I have no idea how my university would do that if I tried. There's no mechanism. And even if there was, that money would go to the university not my lab. So it's useless.

The university wouldn't know what was going on, and there wouldn't be anything technically illegal.

Speaking fees are one obvious way to do this.

Most of the time, college professors don't want anything to do with high school students, or even undergrads most of the time. They only do it because they are told to or there is some personal benefit to them.