I'm seeing so many good arguments for both sides of the fence.
I still say that there was a strong possibility of negligence on the nanny's part. Leaving an iPad on the coffee table where it's within easy reach of a known destructive child is a big part of that negligence.
I'm picturing this possible scenario: Herman was doing whatever Herman does while Nanny was playing on her iPad without paying too much attention to or interacting very much with Herman. Nanny is getting aggravated because Herman is getting aggravated and she finally says "Fine. I'll get you a snack." Nanny puts the iPad down on the coffee table and goes to the kitchen. Herman, seeing the "thing" that's taking up all of Nanny's attention, figures the best way to get Nanny to pay attention to him is to throw the "thing" away.
I don't see this as a far-fetched scenario at all and, to me, it speaks loudly of negligence on the Nanny's part. In the above case, I would not offer to pay for the iPad.
As an employer I think that I would be perfectly within my rights to ask Nanny what was going on when the incident occurred. And I would most definitely ask my child what happened. ADHD, destructive behavior or what have you, the child still has a voice.
Virg -- you keep mentioning the pragmatic thing by doing what's necessary to keep a good nanny. I understand your point of view, however your POV is on the Nanny's side when the nanny might not be that good to begin with. I paid my nanny almost 1/2 of my weekly salary so Nanny was making almost as much as I was. It would really 'hurt my feelings' to pay out for damage that was done just to keep a "good" nanny, when the nanny wasn't really that good anyway. (Okay, how many times can one write the word good in one paragraph?

) When I fired my nanny, it wasn't due to just one incident. Was it practical? No. But it was necessary.
Like I said, a whole lot of strong statements for both sides, but I'll stand firm by saying it's not a
must that I pay for damages until I know further facts.