Does anyone know if there is any difference with public vs private colleges when it comes to security giving you issues?

For example I live in Seattle, WA, and the University of Washington is considered a public university (anyone can protest freely in red square area). I believe in the public university, the police or security can not kick you out because its public property.

On a private property college though, I wonder if a student reports that she is annoyed by a pick up artist approaching women, if the college has a right to kick them out? My assumption would be yes, because its similar to the analogy of mall security kicking someone out. I was told a Private business can kick you out for any reason since they own the property, however on public institutions they can not.

Am I correct on this statement or am I wrong?

I figure for doing day game its best to stick to public colleges to be safe. I once did massive women approaches in a mall one time (about 100 women in 2 hours), and mall security kicked me out for one day only because they claimed the women were annoyed that I was approaching them randomly asking if they were single, and the security said it was disruptive, even though I didn't do anything wrong, I got kicked out for simply approaching. I have never had this happen to me in a public area that is outside of a private property.

I have done day game on public colleges but have not tried private colleges yet.

UW is a public college where I live, but Seattle university is a private college for example.