The credit card is actually a card from my Flexible Spending Account (which is the only reason this hasn't irredeemably screwed my finances for the month) -- given it's limited function and purpose, I haven't checked yet about whether charges can be challenged in the same way.

And if the company can provide me with documentation that I was informed that they can do this (which is all I've been asking them for -- either show me I agreed to this somewhere in the fine print, or refund my money), then I'll accept the charge.