I happen to have gone through this process with a colonoscopy myself. The insurance company rejected my claim. They ended up paying, but not without me spending considerable time and effort to convince them that the test was justified. My brother in law wasn't quite so fortunate, financially. His doctor ordered a biopsy that the insurance company decided was unnecessary, and he ended up paying 1200 dollars out of pocket.
ETA: Just read the response to Professor Yaffle. To try to drag it back on topic, what might happen in the US is that someone will order a doctor will order a high tech procedure, a patient will follow the instructions, and the insurance company will decide retroactively if it was necessary. If they decide it wasn't, or that a cheaper procedure was available, the patient can be on the hook for the full cost.