I went to school back then, and the teachers weren't allowed to hit students. They could send you to the principal for corporal punishment, but his options were strictly circumscribed. His biggest weapon, in fact, was the threat of a paddling.
I can't say that's the way it was everywhere, but they didn't need to rely on that kind of thing - if you made too much trouble they would simply expel you, something I don't think happens these days.
My parents were both in schools where they were physically beat, their fellow students were physically beat, and physical violence was always on the table as a response to student behavior. Their resentment (and the feeling of betrayal by their parents who condoned this behavior) lives on to this day.
So yeah, I think your parent post was talking about public schools. I won't argue that physical punishment (and abuse in some places) was absent from Catholic schools, especially at that time. Missouri also seems to be home to much more conservative Catholics than I'm used to seeing in other parts of the country which may relate to why the teachers/administration behaved that way.
I can't say that's the way it was everywhere, but they didn't need to rely on that kind of thing - if you made too much trouble they would simply expel you, something I don't think happens these days.