This part is why some tire centers will not repair Run Flats:

"· If the tyre has been run at low or zero pressure (with warning alarm active) for a long distance or at
too high speed. This can be identified through driver feedback, worn appearance of the external tyre
shoulder or upper sidewall."

Some places simply do not want to take the liability risk of relying upon "driver feedback," fixing the tire, and then having the fixed tire fail and cause an accident shortly thereafter, because it was run farther/faster than the driver said and there was internal damage to the sidewall. Other places are willing to take this risk, figuring the risk of an untruthful driver and internal sidewall damage that is not visible is low enough.