Well, yeah. As someone once said, "freedom ain't free". If you want to live without Big Brother knowing your every move, it's going to cost you in either money or hassle or both. However, I'm about to obtain medical insurance from a new outfit, and I'm going to try doing it with an assumed name. No one has ever asked me for ID for medical insurance in the past, so if I just pay my premiums on time, things should be copasetic. If not, then they can keep their insurance, and I'll keep my anonymity. I've got enough dough to handle any health problem that comes up.
I'm afraid you'll have to get your kicks somewhere else - because even if you claim to be an illegal alien - they will (have to) treat you. Once again - contrary to what the libs in this country would have us believe - we are a humane people and no one in this country - absolutely no one is denied medical care. The difference is - US citizens have to pay for it themselves while the illegals don't.
I'm aware that they have to treat me. I was wondering if claiming to be an illegal would stop them from bugging me for an SSN. I've observed that some medical centers use the SSN as the master index for their records, which I think calls for a little monkeywrenching.