It's even more mental than that, a friend of ours gave us a story here of someone who hurt their thumb in a bike-crash. They went to an in-network hospital A&E to get it checked out. A&E referred them to a specialist thumb doctor in the hospital for their opinion. They went and asked. Weeks later they get a bill for that consultation because although that doctor works in an in-network hospital, he himself was not in-network (this was never stated nor even suggested, why would anyone question this) they would provide no cover and the friend was now liable for this cost.

You can have the best insurance, follow all the rules, and still get screwed. There is no safety-net.