When is an obligation to pay created?

My wife went into the orthodontist for an evaluation for herself and our son. She understood it to be a free evaluation. They asked at one point if she wanted xray's, she said "sure". After it was done, they indicated there was a fee for this, which she would not have consented to had she known there was a fee at the time. The receptionist stated that the nurse "always" tells patients about the fee. And that it's posted on the wall. I'm willing to fight the "my wife's word vs their word" battle, but if there is really a sign, even if it's in 10 ft letters - which I suspect it's not - at what point is an obligation to pay created? Is this a contract question - offer/consideration/acceptance? Or is this a more grey area?

one related question, I haven't paid for the her xrays via credit card yet, but they already charged our insurance for our son's eval/x-rays... presumably if she signed something that allowed insurance to be billed it obligates us to pay for the amount that wasn't covered by insurance?

If she though it was free then she need not pay--and you may go to small claims court if need be.