I went to a grocery store health clinic without insurance and asked how much it would cost to see the doctor.
They were surprised I asked how much it cost, since they just assumed my insurance would pay for it. After insisting, I finally was able to get them to look it up. They told me it would be $100, but during my exit (and payment) they increased the price to around $200 based on my diagnosis. I asked why it should cost me more money for the doctor to diagnose me with something else, when the doctor didn't do any other special tests (e.g. I wasn't paying for a medical test), and they said "That's just the way it works."
And honestly it makes a lot of sense. The main point of those "we can charge you whatever forms" is because they often don't know off hand what their deal is with your specific insurance company and furthermore they don't necessarily know which people involved are in which network, etc. yet they just want to make sure that you are left holding the bag when the final bill comes due. But if there is no insurance company involved, they only need to decide what they will charge you and it's done. In that case, the open-ended contract is entirely unnecessary.