Now, this puts the burden of proving that the OP's son did the clicking without the OP's knowledge but I imagine - depending how far the OP wanted to go with this - if a sort of diary of the day's events could give a level of back up to the story. So, if the OP remembers that she logged on to ebay, made a phone call to Aunt Sally, ran to the grocery store, came home to make another phone call, went to the neighbors to talk about the cookie exchange and came home to the "you win" email, there may just be cause for mediation to consider the case. Judges make awards and decisions all the time on the basis of diaries such as this - one reason that some executives keep their appointment calendars for years in case they're needed for lawsuits and investigations. My dad keeps his calendars for at least five years.
Anyway, it's not a terribly expensive item and so the lesson to be learned here is a cheap one. Still, if the OP feels strongly about the issue and is able to recreate her day to give support - with some level of evidence like store receipts, phone records, statements from friends, etc. - to her claim that she wasn't around when the purchase was made then she can probably get out of it - if she really, really, really wants to.