You can. I've done exactly this.

Some shady anesthetologists (and others) often try to bill you out of network. In-network charges are subject to insurance company price controls while out of network charges are not.

Once you make it clear you are paying in-network, as you kindly explained to the receptionist (who told you it was all covered), they back down real quick. It's just a scam they try to pull on the uninformed.

What makes you think anyone else would take on the liability of vetting your care for you? And for free?

Because that's how it works in developed countries.

If a law was passed that they have to that's what. If a law was passed that any hospital billing mistake in favor of the hospital should be fined by a 10x fine of the amount on the first offence and a much higher one on subsequent offences. That kind of stuff, stuff that would protect individual citizens when they get sick and are most vulnerable. In a normal country that's what would happen.

The hospital didn't make a mistake in this case; they were indeed covered under the plan. The specialist who is not under the plan is probably not an employee of the hospital. So basically you're saying we should overhaul the way medical billing works. I totally agree, but I don't think that is accomplished by passing a law that levies fines on hospitals.