There's none that I'm aware of that basically anonymizes patient data for use outside of healthcare.

Billing and insurance all falls under HIPAA - those facets and every other aren't disallowed (legally) from things like printing sensitive info - basically if it's being used as part of your care, it's fine.

And students are no exception - when they're on a clinical rotation, they're on that patient's healthcare team and can legally access and print etc that info. The problem is that students still need that data for use outside of that care, and HIPAA doesn't give a fuck about their homework, so any papers that have PHI on it become a violation when they start being accessed for those things. And schools don't trust students not to fuck that up, so they'll come up with overkill-by-design policies like disallowing students from printing PHI, even if it's for use on that clinical and meant to be shredded before leaving. So, the school wants to play things extra safe.

...this isn't to say that insurance companies aren't abusing your data, but can legally handle it within the scope of your billing.