To me, the value of a good FDM system is in having appropriate parameters set to trigger an event alert. If the parameters are set too low, then the risk is that relatively minor events with little flight safety significance are brought to the fore. If all such "trigger" events lead to contact being made with the crew, then this will only serve to reinforce the "spy in the cab" view and will probably end with the loss of pilot support. This undermines the value of the system. Pilots should be encouraged and supported to make their own reports of safety related events, and these can be cross checked against the FDM data to help analyse the event and it's causes.
My current operator has two different levels of trigger event, major and critical. As far as I am aware, only critical events lead to contact being made with the crew, usually as a follow up to the pilot safety report. Critical events should be sufficiently serious that it ought to be obvious to the crew at the time that an event occurred, and an open reporting culture should encourage voluntary provision of the pilot report. Major events I believe are only followed up where the data does not make complete sense, but again, voluntary reports submitted by the crew can be cross checked before any contact should be made.
Both parties need to play the game properly. There needs to be an avoidance of management nitpicking over relatively insignificant events, and a sufficient level of professionalism and open reporting from the pilots, without fear of persecution for honest errors. It requires a great deal of trust, which I can appreciate is in very short supply at times.