Thankfully, only a small part of the academic research enterprise involves human subjects, HIPAA, and all that. Neither fruit flies nor quarks have privacy rights.
Research involving human subjects (psychology, cognitive neuroscience, behavioral economics, etc.) requires institutional review board approval and informed consent, etc. but mostly doesn't involve HIPAA either.
That only applies to government / government sponsored research. That is different from someone doing their own research
This is true, but to say it is "not a law", as you did, completely unqualified, is incorrect. If the research project is connected with a government grant (and many are) you need to pay attention to those laws. Many universities also have their own policies you need to follow, regardless. (Requiring informed consent and protecting people's privacy seems like a good thing.)
Let me repeat it another way. The law only restricts the actions of the government. Members of a university are not the government. Even if they took government money they could legally ignore all of that stuff. Worst case you will not get more funding from them in the future.
I believe you are technically correct, but that does not change the fact that universities have IRBs and will require reviews/approval if you are connected to that institution. You really think they're going to put their funding at risk? This seems very unlikely.
And many, many institutions are over cautious. My own university, for example, has no data classification between "It would be totally okay if anyone in the university has access" and "Regulated data", so "I mean, it's health information, and it's governed by our data use agreement with the provider..." gets it kicked to the same level as full-fat HIPAA data.