Can an In-Network surgeon choose an Assistant Surgeon that does not accept any insurance and bill me the $7000.00 fee the Assistant Surgeon earns?

You did not agree to pay a $7000.00 fee to the assistant surgeon, and presumably the surgeon's office knew you were in-network. It seems perfectly reasonable for them to select an assistant surgeon who was in network, or disclose the fact that the assistant surgeon was out of network to you in advance.

In your case, given the discount that the main surgeon must accept from his or her "rack rate" as a network provider, the assistant would be paid FAR more than the principal surgeon. That's not the deal you signed up for.

I'd consider telling the surgeon the mistake was made by his office, and while you'd be pleased to pay the assistant whatever your health plan allows you, if s/he thinks the assistant should be paid more than that, s/he should pay the assistant out of his/her pocket.

A lawyer's letter may quiet the assistant surgeon.