I don't think this is related to the difference between special purpose use, or general purpose use. I think the problem is like anything else in education - parental involvement will increase children's learning. If the parent works with them to learn how to use the device, I'd bet their scores would go up, similar to a parent who reads to their child or helps them with math homework.
If the parent says "I don't have to teach them anything, the school gave them a computer for that", or "I can't teach them how to use the computer because I don't know how to use it", that child's education is going to suffer. Being computer-illiterate might simply be the current excuse for parents to ignore their children.