I am wondering the same thing because my insurance pays 90% with a lifetime max of $8000. I am pretty sure that you pay more if you self-pay. When insurance is paying, they usually negotiate stiff discounts that fall under the "usual and customary" clause. For example, my statement from Cigna about a toe surgery I had listed the Dr billed $590, then showed the discount and that the insurance paid $136. I owe nothing.
I hope this is the case with this surgery too.