I would take it higher than just the billing department. I would write the CEO of the hospital, and call/write my insurance company, sending everything certified. It could be intentional fraud, or it could be ignorance, but either way, it needs to be fixed.
My coworker just ran into a similar situation with a visit she had to the ER after an auto accident. The auto insurance paid everything but the 94760 that the ER doc billed, because the hospital billed it themselves also, and the insurance already paid them for it. The doctor didn't apply the PO, nor did he record the reading, the nurse did. So how does he think he can bill for it also? The end result is the insurance company is now demanding his chart.
I personally have spent tons of time calling various offices my husband and I have been to when I see something coded incorrectly...consults that weren't consults, 99212's being billed for nurses visits that don't qualify, you name it. It amazes me what gets billed out. And you are right, the average patient has no idea that the 99214 their doctor billed and insurance applied towards their deductible, that they now have to pay for out of pocket, should have a been a 99212. I imagine it is even worse with hospital billings.
One thing I have always told the doctors I bill for is to imagine that every patient is an insurance auditor/certified coder, and to keep that in mind before they go getting creative with their charges.