I work in healthcare-adjacent tech. You can use Claude with HIPAA/PHI. You need to sign a BAA (Business Associate Agreement). It dictates how Anthropic may use and how they must safeguard the PHI (Private Health Information), including not training on it.
I assure you that Claude and other LLMs are used extensively in healthcare, with PHI access, just about everywhere.
Don't be naive. Don't be alarmist.
If anything, LLM use under these conditions is far more safe than the way most people use LLMs. Engineers who aren't under any regulatory regime like HIPAA are using LLMs without the BAA safeguards, exposing personal data directly to the insecure, shared models, which are now training on all the personal data that's being fed into them. People think their communication with LLMs is private and isolated, but without the BAAs in use by companies under compliance regimes, it's not isolated.