Health care for non-EU temporary residents (Lisbon)

I am a US citizen with temporary resident permit here. I received conflicting information about the availability of government health care.
1. SEF's website seems to say that only permanent residents are eligible for government health care. At the same time, SEF instructed me to register at the local health care center.
2. I sent an e-mail to the Department of Health asking for clarification and asking for an appointment. Somebody replied that everybody at the department is too busy to see me and sent me a large spreadsheet. The only applicable iten=ms made no sense and seems to imply that I need to buy some kind of insurance to receive government health care. There is no such insurance as far as I know.
3. Immigration center in Lisbon where they do not seem to know much about US citizens or NHR tax status, told me that I am eligible for the same medical care as any Portuguese citizen paying social security taxes. I am retired, do not have a job and pay no taxes in Portugal.
4. Local medical center registered me without any problem, gave me a sheet of paper with a stamp to that effect and told me that I have to pay double copayment paid by Portuguese citizens.

So the question is if anybody knows what is the rule as a practical matter.