"If Visa then determines that the charge was legitimate, we get the $13.95 back (but not the $25.)"
How the hell would this hold up in court? You legally prove the customer was an asshole and you did everything as legitimately as possible, kept all the records, anything, and still VISA takes money from you? It's not a small amount either, $11.05 per claim. All your competitors need to do is get up a bunch of enough people, or the same people again, say 5000, have them sign up and cancel the charge, and you get a $55,250 bill in the mail.
I say sue Visa.