Yes, this is what I was thinking too, specifically HIPAA (Health Insurance Portability and Accountability Act). I think perhaps a parent or guardian could release medical info about a minor in their care but maybe not. And perhaps LE cannot have access to that info either, without a warrant. I'm too lazy to look up the specific law right now, but I can check at work tomorrow.
I work with confidential information, a lot of which falls under HIPAA--basically, if any document we have has the slightest bit of medical info--from blood type to stubbed toe to died of a heart attack--it is handled in such a way that only people who are allowed to have access to HIPAA info can see it, and that is just for in-house use. You need special authorization to see that info outside the agency, unless one chooses to supply that info to a third party oneself. We would have no right to do so. I imagine a criminal investigation would be different, but LE would still need a warrant.