Another XBox 360 Live question?

Alright, the reason I stupidly don't have XBL is because my mum believes that you can be hacked on XBL. which is true. But she believes that her computer, which she does billing and stuff on can be hacked via the wireless network adapter to her computer. at that point she could get credit card information stolen. Obviously she could use a credit card with low credit for Xbox live, which I'd pay for. So my question is, can your computer be hacked, not XBL account through Xbox Live?