I don't think that's the case. I've anecdotally heard that Stanford does take some (possibly small) amount of equity. From the first paragraph of Stanford's patent policy[0]:

> All potentially patentable inventions conceived or first reduced to practice in whole or in part by members of the faculty or staff (including student employees) of the University in the course of their University responsibilities or with more than incidental use of University resources, shall be disclosed on a timely basis to the University. Title to such inventions shall be assigned to the University, regardless of the source of funding, if any.

For an example of an institution with the kind of IP policy you're describing, the University of Waterloo in Canada has a policy[1] that by default assigns IP to creators rather than the institution:

> Except as stipulated below, it is University policy that ownership of rights in IP created in the course of teaching and research activities belong to the creator(s).

[0]: https://doresearch.stanford.edu/policies/research-policy-han... [1]: https://uwaterloo.ca/secretariat/policies-procedures-guideli...