If they did it that way, then because the attackers had access to the keys
and the server code for an unknown period of time (up to maybe a couple of days), they may have been able to either extract it from memory or use the private key with someone else's credentials to decrypt some or all of the payment information.
I'm really trying to avoid speculation at this point -- we simply don't have enough information to make smart guesses -- but I think we can reasonably conclude that nobody at Linode was manually keying in a password every time there was a charge to a customer card, and therefore it's not insanely paranoid to cancel any cards associated with Linode.
Really the most annoying thing here is Linode's obtuseness about the attack and their processes and what's at risk, and if I end up moving to another service (as at the moment I'm inclined to), that will be the reason -- not because they got compromised, but because they valued their own butts over their customers'.
They're a VPS service for chrissake. They could explain in very technical terms exactly how manager passwords were stored and how the credit card information was stored & accessed and what other billing information may have been compromised -- a full disclosure -- and most of their customers would not only understand most of it, but they would appreciate it.
Sorry, I kinda went off on a tangent there, but the more I think about how this has been handled, the less I feel like I can trust them.