What I believe happens is that people engage the LVL change while in MACH mode. This will make the speed control chase the set Mach number, and since the indicated speed rises rapidly for the same mach number in a descent (as temperature gets warmer and the speed of sound increases as a consequence), the plane will pitch down rapidly to achieve the necessary acceleration. If you disregard the automatic reversion to indicated speed (by setting the MACH mode again after it reverts to SPEED in the descent, for example), you can actually overspeed the aircraft easily, as at some point the set Mach number will exceed the VMO of the aircraft.
Descent speeds in excess of 5000 feet per minute in LVL CHG while in Mach mode is something I have observed regularly in the real aircraft, especially when paired with a decrease in headwind in the descent.
PS: Many pilots did not use FL CHG for the initial part of the descent for this very reason, rather using V/S to initiate a shallow(er) descent until the speed reference could be switched over to IAS and the FL CHG would work more stable.