Happened to a friend of mine who shopped around and got a commitment in advance for the price. He reminded them of their commitment after they billed him for all the extras, and refused to pay it. They withdrew the extra charges.
I contacted multiple hospitals for cost estimates on a simple procedure (hours of phone calls) and only one would actually give me an "estimate." They went out of their way to explain that this was only an estimate and it could easily end up costing more than this due to a number of factors.
I really doubt any hospital will ever give you a committed price for any procedure. I would love to be proven wrong from any other posters :).
You can also show the estimate to other hospitals - this will often loosen them up about quoting a price because they'll want the business.
Typically, indeed, you'll find wording to that exact effect. "This is only an estimate. Actual costs may differ."