that isn't correct, there are plenty of sites that retain this information - just not ALL of it. There are however certain stipulations such as not storing CVV numbers and encrypting your data.
So, in short store the details in an encrypted form- but I have to mention that if you are storing credit card details and aren't sure about the security then I would get some proper advice from a security professional as there are lots of nasties to worry about such as SQL injection and other issues. If the data is sufficiently encrypted then the data is useless to anyone that manages to lift it.
but as silver says, check the PCI docs