This isn't true at all. You generally don't have to worry about credit card theft, you're not liable. ID theft is completely different.

If someone steals your ID and drains your bank account it's going to be much harder and more time consuming to get your money back. If someone opens credit cards under your ID it will be easier to correct than losing your bank account but can still be very time consuming. Often people discover the issue when they're applying for new credit, such as a mortgage. Correcting your credit issues can take months to resolve. They could lose a house they're trying to buy if they don't get approved.