She and her father contacted Apple, seeking a refund for the presumably out-of-warranty iPod. Apple apparently agreed to return the purchase price of the iPod, and sent a letter to the family offering the refund, denying overall liability with regard to the incident, and included a standard confidentiality clause in it.
This is where things went a bit off the rails.
The little girl's father went ballistic, refused to sign, and soon enough, there was press coverage. The Times UK covered the incident, complete with photograph of the girl holding her toasted iPod, accusing Apple of slapping the girl with a "gagging order" and attempting to "silence" them, mafia-style. Whoa, there, Times.
1) This is no gagging order. As nice and evil and meaty as such an accusation sounds, a gagging order comes from a court and no court is involved here. It implies that Apple has gone after this family legally, and that there's been a hearing and a decision and a court order. Quite the opposite. This is just a regular, ho-hum contract between two parties, describing the things they want out of each other.
While the family may be shocked they got a letter, from a legal perspective they should be shocked if they didn't get one. Apple doesn't feel like they've done anything wrong and isn't going to start admitting its products are combustion risks by returning money out of warranty, which is exactly what it would do it if gave money to these people without some sort of settlement agreement.
2) A confidentiality agreement is standard operating procedure. Sure, a letter filled with legalese is a little heavy-handed, but hey, the iPod was out of warranty and when a company agrees to give you money it doesn't feel it owes you, especially in a situation such as this one, it can very well request confidentiality you keep your trap shut about it going forward. It's standard practice even when the company thinks it probably does owe you money. No courts are involved, and litigation is spared where the parties would fight over whether or not the money is owed. And when a confidentiality agreement is sought, it's also pretty standard to remind the parties the possible consequences of breaching the agreement.
Remember: no court is involved here and Apple and this family can reach whatever agreement they want. If the family wants an admission of liability from Apple, they remain absolutely free to pursue a lawsuit in which it will be determined whether or not Apple is at fault. And now, of course, having disclosed all the contents of the letter, Apple I'm sure has rescinded whatever refund it offered.
The UK Times has vastly overstated the standard form letter that Apple sent to them when they sought an out-of-warranty refund. I suspect, however, that Apple could have averted this public relations issue had it said, "look, we're happy to give you your money back. We have no idea why that iPod went kablooey. It could be any number of reasons, including many that don't involve us at all. So if you want us to give your money back, we will, but you have to agree not to discuss it. Why? Because that way people won't think we make defective and dangerous products when it's not at all clear that we do, and giving you your money back is good business, not an admission of liability." And then, when a legal-sounding letter shows up in the mail, nobody is shocked.