Stupid perents will be stupid.
I work with a bank and I have to deal with people calling in about 'unauthorised' credit card charges. Alot of the time when I ask "Well these purchases are consistent and are getting paid back every month. Is it possible that your child/partner has used your card? If so it could be considered fraud and may need to be reported to the proper authorities" people back right down and forget that they even tried to complain about something without even asking first.
The idea of giving your children a smart phone, or even giving them access to yours when you have a credit card linked to your account is just stupid, and frankly it should teach people to be more smart about it. You wouldn't give someone your credit card & PIN so why would you give them access to an account that is linked to it directly?