I can't say for sure, though - I've always gotten very detailed itemized breakdowns of all the cost, hospital stay vs surgeon vs anesthesia vs... but I've never compared them against someone else's bill for the same procedure.
Setting aside the why of the additional expense, the car mechanic model is very similar: you get an estimate, then you get the phone call telling you the additional things they found out, and the new estimate, asking for permission to do or not do the additional things. Though in the case of a surgery where you're knocked out, getting "incremental permission" like that wouldn't really work. You would just have to know the range up front.
But what if the range is so wide to be somewhat useless?
Hospital estimates in the rare case they are provided only seem to get revised in one direction, that seems like having cake and eating it too. If the high school drop out painter can live by his estimates, so can the national hospital chain full of Harvard Business School graduates.
This would be akin to developers saying "Yeah it only took me 40 hours but it was harder then I thought so pay me for 400."