You are ignoring the specific point I am making. Your university can decide any standard it wants for cheating ranging from “it’s possible” to “absolute, undeniable proof.” And that is true for every single infraction except for sexual assault. The Dear Colleague letter mandates a specific standard that is not consistent with the Constitution. When the government mandates that specific action, it turns your university into a de facto agent of the government in regards to that infraction, and thus the mandated actions can’t violate civil rights.
And you keep saying there is no interference, but that simply isn’t realistic. If you are threatening to expel me if I don’t participate fully in a university investigation, without the presence of my lawyer, you are engaging in interference. You are eliciting a response, that could later be used against me in court, via coercion. Similarly, if you find me guilty because a witness was unwilling to speak to a disciplinary panel (for whatever reason), that finding of guilt will be brought up by the prosecution during trial, even though it was made in a situation where I couldn’t compel testimony from a defense witness.
Similar scenarios can be constructed that would harm the accuser’s case in a later trial. The simple fact is that any investigation by an independent body, that isn’t required to follow the same rules of due process, can interfere with a criminal investigation / prosecution in a number of ways. And while I think universities / schools should, by law, be precluded from doing simultaneous or prior investigations, for now I am only arguing that the federal government requiring these things is a violation of civil rights unless all due process rules are enforced as part of those investigations / findings.
Finally, I really wish you would stop raising the specter of universities discouraging students going to the authorities. I have already agreed with you as firmly as possible on that point, and even argued that there should be severe criminal penalties if anyone is discovered doing it. Every time you bring it up after determining we are in full agreement it feels like you are building a straw man.