I think you'll find it's neither: it's usually the owner that has to pay.
I had an R22 that needed spindle bearings replaced, that I'm convinced is due to students/low hours pilots raising the collective with the Governor off: the correlator simply keeps raising the revs. By the time the plonker notices, damage is done. And it's not until 'some time later' that the problem gets noticed.
I think the damage clause is more associated with bent metal (or on a turbine, a hot start - if indeed said machine is fitted with a hot start indicator light): much easier to prove than a rotor overspeed.