Using a processor who stores the card number outside of your infrastructure (ie. Stripe) can also be helpful.
Card vaulting as a service: https://spreedly.com/ ($10/mo for up to 5000 cards)
Also you're fined by the credit card companies if you lose card information. I believe it's a per card fine, so it get expensive really quickly.
Actually I don't get why any company would choose to store credit card information, when most payment providers will do it for you.
But yes, significantly better than other situations.
But if that happens, it's not your responsibility (at least not 100%), it's theirs
Much like Linode are responsible for hosting my clients site but I sigh am accountable when something goes wrong.