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.