What insurance company is it? Almost all have a customer advocate team which can help you navigate around the standard 'can't help you' response you get from the level 1 customer service team. I would call back and ask them if you can speak to a customer advocate associate. Then, after explaining to them the runaround you got from the provider, I would file an official appeal with the insurance company to consider those docs and lab as 'in-network' even if they have to get an approval from the plan sponsor (is this insurance through your employer or your spouse's employer - or through an exchange)? It's worth a shot.
After all that - I would take my business elsewhere for future appointments as it sounds like the practice is purposefully confusing patients on in-network and out-of-network status. Not sure what is behind that but you did your part by verifying up front the in-network status.