Medical billing is so convoluted.
I split my eyebrow open after slipping in the shower around 8 PM one night. There was one urgent care near me that was still open, so I went there. The cut needed stiches, but the urgent care doc didn't feel comfortable doing them on my face. They suggested bringing in the on-call plastic surgeon, who was out of network. I actually have pretty good coverage out of network, so I decided to take my chances. The plastic surgeon cut it open a little more so the wound was straight, and then did a great job stitching me up. You'd never be able to see the scar unless you were looking for it. He ended up being super kind about the billing. His office "charged" me a huge amount to get the max they could from my insurance company, and then wrote off the rest and zeroed out my account. I don't think they ever even asked for a copay or coinsurance, even for the follow-up visit at his main practice to take the stiches out.
Any chance you did see an unusual specialist at your urgent care visit? Though they should have notified you if they were bringing in someone who wasn't covered under a normal urgent care visit. Also, have you tried contacting the urgent care itself, or the doctor? Insurance can't change how the visit is coded, they can only tell you what they owe for the code used. Hopefully a conversation with the office's billing department can clear things up. Maybe they're charging you to get money from insurance and aren't expecting you to actually pay. But whatever happens, I wouldn't just ignore the bill. At least whatever happens it's cheaper than an ER visit.