At many universities (in the U.S. at least), on paper, it’s the technology commercialization department that makes the call about pursuing patent protection and the burden is on the PI to report all potentially patentable inventions before release so that the university has time to make the determination. In the case you describe, they’d in principle find you in violation of that policy, but in practice can’t because they don’t know about it unless you tell them.
Yes, I think you're right. It _depends_, as always. Mostly on the field, and in my case, on country. I am in Germany and Universitities are mostly State financed. There has been a pretty liberal trend at Universities in Germany the last 10 to 20 years, pushing towards open science for society (any society, not just Germans). We have such a department you describe, too, but no one has ever heard of it and its not really used, or lets say regulations exist but are not enforced. The University itself also pushes for Open Source publication and free sharing of results and technology, except for rare cases.
