1) Those that are glorified private security firms
2) Those that are actual police with authority to arrest and investigate.
If you go to a school with type (1), they are much more likely to violate these rights as they have no real investigative authority outside the university judicial system. You can sometimes have issues with (2) if they know they will just be referring your case to the internal university judicial system, but they are often more professional in getting any evidence cleanly.
The only reason they should care about the law of the land is when they themselves are violating it, and there is no law that says "all private police and prosecution must also abide by innocent until proven guilty".
But colleges don't follow due process.
What happened to:
"The law presumes all innocent of crime until proven guilty." (Source: Law Reports of the Supreme Court of Ohio, 1835)