It's very easy to confuse vertical bounce with rapid fore and aft movements of the cyclic - several Squirrels (AS 350) were snagged for vertical bounce when I was the MTP. They all turned out to have faulty vertical gyros which, at a particular pitch attitude, would produce this effect. Thus, I still feel the most likely reason for the situation was the stude simply overcontrolling in pitch - easy to do with both APs out on a 412 (and I still think it's a daft thing to do).