Start by calling billing and telling them what happened, and that you effectively don't have insurance and will be self-paying (said for the purpose of negotiation, not what you may or may not actually do). They should discount it by a lot.
Healthcare providers have starting saying it's "insurance fraud" to say that you don't have insurance when you do.
My guess: they know they can get more money from the insurer than the individual (or a combination of both!) so they want to scare you from not allowing them to negotiate with the insurers.
