From what I've read of this case, it sounds like they've "stretched" this law to fit the crime, mostly because there was no other way they could hold the mother accountable for the girl's suicide. In this case, at least, I'm with the prosecutors. Otherwise, the woman would go without being charged for any wrongdoing whatsoever.
Not really. The issue at hand is the MySpace Terms of Service.
MySpace owns the servers that their site runs on. They give people permission to use those servers only under certain circumstances. The permission to use those servers is contained in the Terms of Service.
Some of MySpace's terms say that you can not lie about your age, and you can not use their service to harass, threaten, or intimidate anyone.
When you violate the terms of service of an online provider, you do not have permission to use their servers. Using someone's servers without their permission is a crime; if it weren't, then it would be impossible to prosecute any case of computer hacking. The defendant in this case created a profile that lied about her age, and used that profile to harass another person. Those are clear violations of the MySpace terms; ergo, she did not have permission to use the MySpace servers.
People can and have been prosecuted for a lot less. For example, people have been prosecuted for using someone else's WiFi router without permission. This case is much more clear-cut and far more straightforward than those cases!