I didn't think about that. So essentially, the credit card issuer didn't really spend "their money" at all. Wow. The more I learn the more I realize how little I know.
Afterwards, if you do a chargeback, the bank will yank back the funds from any other amounts the bank owes the merchants, but if the merchant has enough proof the cardholder participated in the transaction (aka, swipe and sign, or chip and sign, or use of CVC code online), then the bank will give the money back to the merchant. The bank still takes $30 or so from the merchant as a fee for getting a chargeback though, but I'm sure that amount and terms vary from merchant to merchant, depending on their purchasing power.
A friend told me about this case where a vendor charged his American Express twice. They called the vendor about this and the vendor yelled at him so he called American Express for a charge back. Apparently, American Express went in and did a charge back for the whole amount. I am glad they did the charge back but it must suck for a merchant if the charge was legitimate and the customer was being a jerk.
They might ask for payment up front, but they'll quite happily take a credit card instead. Yes, credit cards are a form of transactional debt if you pay them off each month; they allow you to enjoy your purchases for ~ 1 month before paying for them.