https://www.visa-bkdeal.com/register.aspx

Prior to participating in this program, online registration of a valid Visa check card or credit card on the registration page of this site is required. Upon qualified registration, use your registered Visa check card or credit card at any participating BURGER KING� Restaurant for 10 purchases between June 1 - August 31, 2007, and receive a credit for the amount of every 10th purchase (up to $7.00 max value) on your future Visa check card or credit card statement. No minimum amount required for any purchase. PIN-based purchases, Visa prepaid or gift card purchases, ATM transactions, cash withdrawals, and purchases made outside participating U.S. BURGER KING� locations do not qualify. Offer valid only on purchases at participating U.S. BURGER KING� locations with U.S.-issued Visa check card or credit cards.

Do they serve Phish?

This sounded funny to me too, so I went to the visa.com website. I think this is actually legit.

Here is the url which redirects to the one the OP posted:
http://www.visa.com/bkfree

I heard about this on the radio, as well.

Of course, this offer requires actually eating at BK... no thanks.

Three Dallas area Burger Kings (Frisco, Corinth, and Flower Mound), have just been added to Rewards Network (IDINE). You could combine this promotion with the various IDINE promotions and get extra miles if your VISA is registered with Rewards Network (United, Delta,...) as well.

There may be many other Burger Kings that are also IDINE. A quick search also showed 29 Philadelphia and 6 Miami area IDINE Buger Kings.

Don't forget that your VISA has to be registered for this promotion as well as for Rewards Network.