I'm concerned about the point of view that if the nanny is in charge, she is responsible for any damage the child does.
If the nanny takes the child out in public, and he damages something, would we expect her to pay for it?
Suppose she takes him to a children's matinee, and he throws a Coke on another patron, who wants his clothes dry-cleaned. Would the nanny be expected to pay for that? Should she be expected to predict that giving him refreshments would lead to him throwing them?
Suppose he took off his shoe and threw it at her plasma TV. Would she be responsible for paying for the TV?
If she were babysitting him in his home, and he throws something and breaks it, would she be responsible for reimbursing the parents for their property?
I think you'd have to be paying a nanny a lot more than most nannies make, if you were going to expect her to assume financial liability for any and all damage the child does while in her custody. As someone pointed out, it's impossible to watch a child every minute, without being the sort of controlling person that would probably infuriate most 4 year olds (never leaving them alone, making them accompany you to the bathroom, stand next to you while you prepare meals, etc.).
It is not my view that if the nanny is in charge, she is responsible for anything the child does.
It _is_ my view that if the nanny is in charge, she is responsible for taking reasonable precautions to make sure my child is kept from things that my child could damage, or could damage my child. Let's move away from the OP and assume the nanny is in charge of a typical 18 month old. If she has assumed responsibility, assured the parents that she is experienced and capable of taking care of an 18 month old child, and then takes the child to her home, I would assume that she has taken the precaution of removing any glasses, vases, , scissors, small choking hazards, etc. These are all standard precautions for taking care of a child at that age and development level, and if I arrived at her house to discover her outraged that my child had knocked over her precariously balanced Ming vase, I'd think the nanny had been a bit careless, and I don't think I'd offer to fork over a pile of money to replace it.
I think the question comes down to whether or not the iPad could have and should have clearly been kept away from this child. Now in terms of 'could', iPads are small and easily movable, so I don't think there's any reason that it _had_ to be within reach of the child. ( If the child had smashed their large-screen TV, I'd consider that the parent's responsibility as the nanny can hardly have been expected to re-decorate her house prior to the child's arrival ).
So should the nanny have known better? We just don't know from the information in the OP. If this is a child who frequently acts out, breaks things, destroys things, and the nanny has full knowledge of that, then she does bear some of the burden of trying to keep these sort of events from happening. That would be - I assume - part of her job description, and part of the reason she was hired.