The Supreme Court, interpreting the protections of the Fourteenth Amendment broadly, have recognized that not only are people protected from abridgment of their freedom of speech by Congress, but are also protected from abridgment by state governments as well as creatures of the state such as cities and counties. This would include publicly supported colleges.
The idea of "free speech zones" suggests that there must also be "prohibited speech zones". Not a good idea.
In support of his case, the student should arrange to have someone passing out pro-abortion or anti-Trump literature under the same circumstances. It wouldn't surprise me a bit if this strengthened his case considerably.
In interpreting the First Amendment to apply to any other entity than Congress, the Supreme Court is modifying the Constitution; this is outside their authority and, according to Marbury v. Madison, that a law* repugnant to the Constitution is void, and that courts, as well as other departments, are bound by that instrument.
* -- Or judicial act, if you apply the same logic as presented therein.