Do you think that you need permission from your university to do meaningful research?

Sure. Who is to care what you do in your basement?

Yep, you can do that. Who is going to pay for the materials?

To do research under the banner of the university, they don’t need permission unless there is an ethics consideration. If the work involves any animals (that includes humans), they have to submit a proposal to the university for ethics approval.

To use equipment belonging to the university, the student needs either the permission of the university or the permission of the prof in whose lab the equipment resides. Usually the university isn’t directly involved in that.

This is assuming the project costs no money or that the student (or the student’s supervisor) is paying for the research independently. As @zenvelo points out, if the university is paying, then the student “needs permission” in the sense that the university has to choose to fund the student’s proposal over those submitted by other students. The university doesn’t just automatically hand out money to everyone.

You need permission for money, and you need money for research.

If the research involves people (or even data relating to individuals), you need permission.

My university all you had to do was propose an idea for research that was new or cutting edge and you could get support for it. Professors want to be published, for many of them it’s publish or perish.