When I complain they offer me a "courtesy credit". Or I don't complain and just don't pay since if they can't be bothered to bill me correctly, I can't be bothered to pay.
So yah, admin mistakes. Deliberate ones.
Insurance just pays, they don't check the coding as carefully (how could they, they were not at the appointment).
An extremely common "mistake" (up-coding) is increasing the length of the Dr. visit up a level or two. Take a watch with you, and check how long the Dr. was actually present with you, then check the coding. (And paperwork and nurse time is built in, so it's not necessary to account for that when checking.)
They'll also bill for services they talked about, but didn't actually do.
And they'll code separately for a service that's supposed to be bundled with another code.
I've seen every one of these.
The US health care system is crazy in many ways, but hospital/doctor office billing and admin is one of the more egregious. I firmly believe they make money by people simply paying every statement they get, some of which the insurance company will later take care of anyway, just out of fear of these "collections"