mross,
There's something called FDM in the aviation industry:
Flight Data Monitoring!
Pilots in most companies will get invited to "Tea and biscuits" with the "Chief pilot" when he/she significantly exceeds normal flight parameters, without even getting close to flight envelope protection!
When a pilot messes up so badly that flight envelope protection has to kick in, it will be known! And yes, this will happen only very rarely!
Of course, not all of these very rare occurrences will make it to the press, and you and I might not hear of it. The simple fact that reaching the flight envelope protection is very unlikely, is, by logic, enough to say that these events occur only very rarely. Back to topic now, please.