We are obviously following different procedure paths, but yes you are correct we fly our aircraft with exceedances above thresholds every day otherwise they would never get off the ground. I would be mightily surprised if you did not either as exceedances are regular occurences.
Are you talking about 'real exceedences' or spurious spikes that indicate a faulty accelerometer? If the latter, then that is simply a normal use of the MEL to allow flight with a defective HUMS system (10 hrs or 25 hrs depending on whether close monitoring is in place.) If you are talking about HUMS exceedences that are considered real (following a trend for example), then I'm somewhat astonished - to put it mildly! Or, are you talking about low level thresholds, in which case you are simply close monitoring the HUMS system, as it is designed to be.
Either way, I see no reason why the pilot should get involved in the process, and don't believe the logic bears much scrutiny. The same logic would apply to wear tolerances on mechanical componants, leak rates, crack propogation etc etc.