The debt argument is perfectly valid, but in the US, you're not liable for fraudulent charges on your credit cards. The maximum liability is something very small, like $50, but I've never had a bank hold me liable for a single penny in fraudulent charges. This is because the banks simply charge the fraudulent transactions back to the merchant. The banks are not on the hook for the money, so why would they care?
If you cancelled your credit card after the Linode breech, you potentially saved yourself some hassle, and you saved some merchant somewhere the trouble of a chargeback and lost merchandise, but that merchant wasn't properly verifying cards anyway, so it's still on them. You didn't save yourself a penny.
All of this assumes that all the cards were actually compromised. One report of suspicious activity -- no matter how tightly constrained this person was with their usage -- does not prove that CCs in the Linode database were compromised.
Personally, I don't really care. One of the great things about credit cards is that you're protected from fraud (no really, that's one of the big sales pitches they make). Linode says the cards were encrypted and the private key had a strong password. I have no impetus to inconvenience myself until there is some material reason.