Just thought I'd support jksflyer. Whilst clearly the invalid credit card has caused you significant problems CJKatl I have only benefited from the policy of not swiping a card at check-in. At my regular hotel it lets me breeze in (I get an envelope with my pre-cut room key which cuts checkin down to about 5 seconds as the staff notice me walking in the door and pass my envelope....). I suspect you could ask for a note to be made on your file if you don't want this to happen but for most guests I imagine it is an advantage rather than a disadvantage (and makes you feel a valued customer over 'normal' guests who are not trusted and have to have their card swiped - many of us are probably in a more simple situation than yourself though, so I use only a single card for my checkins , and sometimes change the checkout card (but don't mind if it is accidentally charged to the wrong card)
However, I had an unfortunate credit card expiry earlier in the year (for the card I gaurenteed all my reservations against) that meant I had to ask a poor plat desk agent to change around 30 reservations from the new to old card - but this happened smoothly and easily without any follow through problems!
Also, hate to say it but;
The hotel should never assume what card they think I'm going to want to use to charge the stay
Surely if you make a reservation and gaurentee it to a card then the logical choice for a hotel would be you want to use that one for the stay itself - most customers probably only have 1/2credit cards anyway (even I tend to close down a card I don't use once I've got the bonus points I want out of it) and would use that card for the stay.
BUT - let me be quite clear - once the problem was identified the resolution should have been simpler, and also less troublesome and appreciate the problems you were having.
PS: You mention a third number... is that another card on your profile they chose as the first card had been closed?