Must be a pre-dock connector iPod, and therefore only uses firewire.
You could always just remove iTunes from her machine....
can't you just connect it to your computer and pull the songs off? then either hook the computers up over a LAN or burn off CDs or DVDs of the MP3s. Don't tell it to sync, then just use Terminal.app to copy the songs off. That's how I moved all my MP3s to my new computer when I got it, since I didn't have the facilities at the time to hook them both up at once; just connect, don't sync, and then copy.
However, I'm still not sure that syncing will delete songs off the iPod to match the computer's library... although it is better safe than sorry.
Also, tell her you know how to fix it but won't unless she tells you how she deleted them. It's such a bad habit to be in, telling people you need help fixing things and then not telling them how you messed it up.