The pilot, who held a private pilot certificate, was receiving dual instruction from a certified flight instructor (CFI) to become familiar with his newly acquired tail wheel equipped airplane. After practicing some standard flight maneuvers at altitude, the pilot returned to the departure airport to practice full stop landings and takeoffs. The CFI demonstrated the first landing, and then the pilot performed the next four landings and takeoffs with the CFI monitoring the controls and providing assistance when necessary. The CFI stated that the pilot's first landing was normal, the second landing required minor directional control assistance, the third required no assistance, and the fourth required some assistance from base leg to final but the landing and roll out were normal. On the fifth landing, the pilot made a nice three point touchdown and rolled straight ahead. During the roll out, the airplane suddenly swerved to the right and the CFI immediately saw that the pilot had already had full left corrective rudder applied. The CFI then applied corrective left brake to try and correct the swerve, but the application seemed ineffective. He then applied right brake to try and slow the airplane's pending departure off of the runway. The aircraft then pitched over on its nose, then over onto its back, coming to rest in a snow bank that was bordering the runway. The top of the rudder sustained substantial damage. The airplane was equipped with a STC non-standard brake system. The CFI stated that when he had ferried the airplane, he noted that the brake system had extreme sensitivity. The CFI stated that he told the pilot early in his instruction that the use of the brakes should be avoided in normal operations due to their sensitivity. The CFI stated that he believes that the sensitivity of the brake system was a causal factor in the accident.