I'm sure equill will be able to provide a great deal more about the chemistry, but it is my understanding that over-discharge is dangerous because conductive filaments can form in that condition, and short across the cell. Charging a lithium-ion cell that has these filaments will result in a fair amount of heat generation, which for Lion cells is a Very Bad Thing.

The threshold for determining if an over-discharge has occurred is necessarily set to a safe value, but such conservative controllers will prevent you from ever using that battery again, even if it is actually salvageable.