"All this is to say that the nanny knew the kids behaviour and was responsible for the behaviour of the kid under her watch. The parents are not responsible for the "bad" behaviour. Some kids are wired differently and the best parenting in the world may not be enough to prevent violent outbursts."
They don't bear blame for not preventing the outbursts of their child, but they bear the responsibility to deal with the consequences of their child's actions. I see this the same way as someone's child throwing a ball through a window while he's visiting someone. Sure, one could argue that the nanny shouldn't have left the iPad in reach, but we must not forget that she took the boy to her house as a favor for an unusual situation and as such there's got to be more responsibility on the parents because their situation is what caused him to be there in the first place. If the nanny normally had Herman in her house then she's deeper in responsibility for childproofing but it was a one-off, and as others said what about any of a hundred other items that she may not have been able to remove or protect like lamps or her television?
"Yes, in the child-care business accidents happen. I guess, in the long run, it's up to the parents to decide whether it was negligence on the nanny's part or to pay for the damage just because that's the way their child is."
This sounds like a good way to end up without a nanny, to be honest. Look at it from the completely pragmatic view. What nanny would consider it worth the risk to end up working for a week for free any time they had something like this go wrong (or worse if he managed to wipe out something like a television or break the faceplate of her oven or whatever)? Would the same parents ask her to pay for broken stuff in their home if Herman destroyed something while she's watching him? I know for certain that if I was the nanny in this situation and payment for the broken iPad wasn't proffered directly, I'd quit and find a child less likely to destroy my stuff and parents less likely to force me to pay out of my pocket for it, because the danger to my income would simply not be work the risk.