The punishment needs to be commisserate with the crime, and dealt with through due process; to do otherwise is distinctly un-american (see 1st amendment on freedom of assembly, 4th amendment on freedoms from unreasonable state actions: "The right of the people to be secure in their persons[...] against unreasonable searches and seizures", and especially the 5th amendment: "[no person shall] be deprived of life, liberty, or property, without due process of law").
What we are seeing at Colombia University (as well as the country at large) is the continual abridgement of these rights. Note that for the fifth amendendment specifically, the constitution refers to any person, not just citizens. Those here legally are entitled to due process protections under the law.
The following argument relies on the following: (1) Universities historically have been the the catalysts of change through student protest. (2) Peaceful protest is a right of the people that shall not be abridged. (3) Public Universities (being government institutuions themselves; see campus police and jurisdiction) have a duty of care to protect their students.
With the above holding true, the argument against this being a "betrayal" falls facially flat, as it is a severe consequence that the university capitulated to, and had a duty to prevent. The arument boiled down to "they were being disruptive, so we should get rid of them," because the betrayal amounted to the jailing and deportations (or attempted deportations, in some cases) for the "crime" of being nonviolently disruptive in a public place.
Without articulating a legally rationed basis for a criminally sanctionable offense, an equivalent is threatening to jail and deport construction workers when they block a business entryway. In general, you do not have a right to be merely inconvienced by others in a public space.