As a part time delivery
captain, I've never asked anyone about their
health insurance. For the tiny amount of time spent out of the country (getting boats up from Mexico) I don't mind taking the risk. Long term international coverage is a separate discussion. On the plus side
medical insurance is about 1/7th the cost everywhere compared to the United States. That is essentially the root problem in our whole
health care problem: the costs are just astronomical.
It's not really a question or topic that comes up, that I've noticed. You're on your own. The only thing a captain should know (and should ask) is if you have any conditions relevant to the task at hand, and any medications you're bringing.
You can pick up short term international insurance dirt
cheap. As far as being out of state, that depends entirely on your insurance plan.