First, the healthcare market is nothing more than a government regulated racket. However, even if it was fully free market and you didn't want to pay somebody to provide their time and services to save your life, that's not their problem. You can't enslave people, even to save your life. And relating this to coercion because somebody won't provide a service to you without you compensating them is just trying to force a definition onto something you don't like.
Second, a local government forcing you to move in order to not pay a tax you don't want to payis coercion. Plain and simple. If you don't pay the tax, they arrest you.
So scenario 1, you don't pay for a service, you don't get it.
Scenario 2, you don't pay for a service you're thrown in jail.