I have admired Strauss’ comments. But I would not argue that colleges have to respect constitutional rights simply because they are constitutional rights — and DeVos does not make this argument.
Rather, I think they have to avoid gross injustice simply because injustice is morally wrong. The argument is that these pressures and regulation lead to a system in which someone can suffer extremely serious consequences: being expelled and having their reputation ruined, tarred for life by a “conviction” (as it will inevitably be seen) as a rapist or sexual assault perpetrator — but all on possibly flimsy grounds by a fundamentally biased process. That is unjust and so morally impermissible. If it makes sense to have those rights in criminal trials, then you have to have them in any quasi-judicial proceeding that can have similar consequences for basic fairness. They are there to protect against injustice.
That would be my best version of the argument anyway.