On the CO site under credit cards it says
First checked-bag fees automatically waived for primary cardmembers every time you fly on Continental-operated flights and pay for your tickets with the card (a savings of up to $50 per round trip per passenger checking bags)*
though in their page on baggage fees it says it will be waived for
Continental Airlines Chase primary cardmembers will have their first checked-bag fees automatically waived
without saying you need to charge the tickets to the card. So it appears it is based on which webpage you print out and bring
