Determine credit card type by number?
I have heard one good reason to make them pick (even though you can figure it out). So that they know the list of credit cards you accept.
As a consumer, I hate choosing a card first. I want to just start typing the number.
This issue is discussed in Wroblewski's Web Form Design on pages 153-154. It's in the section "Removing Questions" of the chapter "Unnecessary Inputs." The example given is Paypal, which highlights the type of card when you've typed in your number.
Yes, the site you mentioned is correct. Many sites, incl. Google Checkout I believe, rely on automatic detection of the card type. It's convenient, makes the UI less cluttered (one less input box) and saves time. Go ahead!
I am pretty certain that at least for MasterCard, Visa, Discover, and American Express that that is accurate. I have never worked with any of the others.
See the very bottom of this page: http://www.merchantplus.com/resources/pages/credit-card-logos-and-test-numbers/
Also this might be useful to you" http://www.beachnet.com/~hstiles/cardtype.html
This is pretty interesting to: http://en.wikipedia.org/wiki/Bank_card_number