Are you sure you don't make this up? Any insurance that I've ever had always let you search if a particular provider is in their network. I just verified on the website of my current insurance. Dozen of anesthesiologists nearby are listed. In fact they often go out of their way to notify you if your doctors leave their network.
See for example https://www.reddit.com/r/personalfinance/comments/ho49d5/ane... - first hit of many for “anesthesiologist out of network”
Especially if you have an emergency surgery it’s not like you’re picking your anesthesiologist from an approved list before entering the OR, even if you took the time to make sure the hospital you visited is in network.
Finally look at the fine print for your insurance company’s website. You’ll see multiple disclaimers noting that the information may not be accurate - for example from blue cross blue shield:
> Blue Cross and Blue Shield Licensees have made reasonable efforts to ensure that the list of providers displayed is up to date and accurate. Please call the provider before making an appointment to verify that the provider continues to be part of the network.
Then when you call the provider to confirm, they shunt you back to your insurance provider. It’s hilarious if it didn’t have significant financial consequences.
Oddly enough, I had the exact opposite experience recently, doc's billing dept said specific medical appliance would not be covered so I had to pay out of pocket, only to find out later it was reimbursed by insurance and I got refunded for my out of pocket cost.
Had experience with that too. Insurance company will not give you a straight answer as to what’s covered or not- as for example the anesthesiologist may be out of network and you’ll never know until it’s too late. The health care provider won’t give you that info either. So you end up rolling the dice and hoping it all is covered at the end of the day.