It's not that ridiculous. Securing stuff on computers is more important due to the scale at which attacks can occur. On the internet, you can gather information on millions of users in little time and without putting yourself in a place where you could easily be caught. And for a machine that isn't connected to the internet, it can still give you far more data than you could get by stealing paper that takes up the same amount of physical space.
I'd say most of the parents' comment is applicable to the same scale. People can abuse your social security number or bank account and routing numbers across the Internet. Phone numbers being relatively easy to spoof and/or hijack makes fax trivial to mess with internationally as well.
