Billed for surgical assist for C-section that insurance refused to cover

I am located in Texas. My wife gave birth to our twins back in May of this year via C-section. We had insurance and ended up hitting our out-of-pocket max which we paid months ago. We just got a bill for $300 from a separate company (not the hospital) that provides first assists for surgery. Apparently, one of the forms my wife signed while in the hospital prior to giving birth was a consent form for this first assist. In the fine print it states that my wife understands that if our insurance doesn’t cover this cost, that we are responsible for it. Our insurance has denied their claim and they have sent us the bill, but this seems like a pretty clear instance of balance billing and I don’t think we should have to pay if our insurance won’t cover it.

We signed a stack of forms in the hospital and to be honest we didn’t read them all that closely as my wife was in labor. Is there anything we can do to avoid paying this or should I just count myself lucky it’s only $300 and pay it?