When Costco announced they ended their relationship with AMEX, they announced they had a relationship with Capital One. I happen to have a Capital One mastercard in my wallet right now with my picture and costco # on the back, so it would seem you don't know what you are talking about.
Now, to add a bit more info. Since Costco now accepts Capital One Mastercards, that means they accept most if not all Mastercards, but only the Capital One cards with your picture on the back can be used in lieu of the actual Costco card.
Anyway, the way I posted is 100% true, and that is why my Mom was shocked to be turned away. That is also why she didn't carry her actual Costco card because the literature that arrived in the mail indicated she would be able to use the AMEX Costco card until Dec. 31.
Thanks for calling me a liar though.
http://www.capitalone.ca/credit-cards/costco/