I think there may be a element of this, particularly when a student's family has donated substantial sums to the university, but I don't think it applies to the vast majority. A university's reputation is worth far more than tuition fees, and at institutions like Oxford, there are always plenty of others who would gladly take the place of anyone choosing not to attend just because Oxford took a firm stand on a protest.
Something similar happened at Stanford Law School a few years ago and at Yale Law School before that. Both schools charge high fees.
The next day, Stanford's law school dean put out a statement affirming the school's commitment to freedom of speech. Stanford's president and the law school dean apologised to the speaker two days after the event.
https://www.insidehighered.com/news/faculty/academic-freedom/2023/03/12/stanford-apologizes-after-students-heckle-judge
The dean later put out a more complete statement affirming Stanford Law School's commitment to free speech and robust debate.
https://stanfordmag.org/contents/the-first-amendment-does-not-give-protesters-a-heckler-s-veto
At Yale, the school read a statement about its free speech principles and protesters exited the event before it started.
Debra Kroszner, a spokeswoman for the law school, in a statement said that after the moderator read the university's free speech policy for the first time, "the students exited the event, and it went forward."
"Members of the administration are nonetheless in serious conversation with students about our policies, expectations and norms," she said in a statement.
https://www.reuters.com/legal/legalindustry/conservative-judge-urges-us-judiciary-not-hire-yale-protesters-clerks-2022-03-17/
I think the idea that leading universities are going to pander to students because of high tuition fees is wide of the mark. I expect Oxford to issue similar statements in support of academic freedom and robust debate soon.