Do not go through United trying to get them to pay this. Prepare for a day spent on the phone with the hospital until you find the person in the billing or services department who can really get to the bottom of it. They will figure out for you which technicality the insurance company is trying to use and what the correct one is. I had something similar happen and, after a day on the phone, was able to get the incorrect code that was used, how much they were supposed to pay, and what to say to them (this needs to be reprocessed according to X agreement).

From there you need to write a letter to United saying you want the case appealed. Send it certified mail and be prepared for the first response acknowledging your letter and the second one, about 30 days later, with the result of your appeal.

PS: I would have emailed this to you but couldn't find any contact information in your profile.