Busting Minimas may not be very uncommon especially in operations where Flight Data Monitoring is not in vogue. One can see just such an example in the recently released investigation report of the CRJ accident, available in African Aviation Section of PPrune:
http://www.pprune.org/african-aviati...-dr-congo.html
While busting Minimas by a little bit, the crew may believe that he/she is not going to cause an accident, he/she may believes that it may be a way to get the job done.
But Minimas are supposed to provide the safety margin, hence any compromise on Minimas reduces the safety margin.
On most days, one may be able to get away but when chips are loaded against you, busting Minimas may be just another factor in the accident.