Well,I have mixed opinions on this subject. On one hand Microsoft has no idea of whether a kid is playing a system or the card owner (game consoles are not just for kids), on the other hand I've been thinking about this and while I've spent quite a bit on XBL over a long period of time, I'm not entirely sure what you could do to run up a bill like that so quickly. I mean what did he wind up buying?
I'll also say that I think the credit card company bears some responsibility. I say this because credit cards advertise security protections, and I've gotten several calls using my card legitimatly to make purchuses, especially in the past when I ran up a lot of my personal debt (while working, I didn't plan to become disabled)) and spent a lot of money at one time. Truthfully if she wasn't purchusing XBL stuff except for that six month period, I think that by rights the card company should have at least made a couple of calls to ask about these charges. Heck, I got a call for when DCUO verified my card by putting a $1.00 charge through to test it.
You could say that this is a responsibility dodge, but let's be honest, these cards promise customer protection, by their own standards they should have verified this change in purchusing trends at some point. One of the reasons why this exists is in case of someone like a kid using your card without your knowlege, like if your 40 years old and your teenage daughter "borrows" it to make a purchuse at Hot Topic.
Otherwise, it is pretty much her fault for not paying attention. What's more one of the big reasons why they have pre-paid cards for things like points and gold memberships is specifically so parents don't have to put their credit card information into a kid's console. This isn't even an obscure piece of information, and while entering the credit card info she should have noticed the bit about pre-paid cards (to enter the code) if nothing else. Of course it's possible that "mom" is rather dumb herself, or is running a scam. I mean one of the reasons why companies like Microsoft don't give refunds in cases like this is because of people doing things like running up huge bills, and then claiming "my kids did it" and effectively getting all that stuff for free if they provide the refund. Sure, people suffer in legitimate circumstances, but that's the problem, you can never tell in cases like this. I mean a crook in cases like this is always going to insist that they are a victim, and her going to the press (which is why we hear about this) to put pressure on Microsoft seems a little 'iffy' to me.