to the ER, they've probably done their homework to make sure they are going to an in network hospital. But after that, who would stop the ER doctor and say "wait, are you covered by my insurance? If not, can you find a doctor that is? Considering how complicated networks are (a doctor may take an insurance but only be in certain networks within that insurance, for example), it wouldn't surprise me if the doctor could even answer that question on the spot.

At least with an appointment there can be some research done in advance - which is something an ER patient doesn't have time to do (or the wherewithal to think about in some cases).