Uhm, well being "convicted" of breaking a rule means exactly what? It makes no difference if another student says it, a teacher says it etc, the Dean in most cases makes the final call, noting that it many cases there is a student appeals process etc.
I am not sure they get the "tried" portion in most cases, however it could be a disciplinary hearing with a board oversight, likely depends upon the institution.
The security forces without police powers can already do that same thing, less the arrest beyond a citizens arrest. It is in fact more protective of students rights to have a police force vs a security force in some ways as a police force must have PC to search without a warrant, a security force does not need anything to search university property aka dorm rooms etc.
There are some really good reasons to step to the level of police over security, however it also does lend itself to another level of governing of people and while typically non-restrictive, that depends upon view as mentioned earlier all other rights seem to have merit but 2a rights so they also typically fail in that area. Notably, that is not always a "liberal position" type of choice and within some accrediting guidelines it must exist.
