[PHXFlyer]

Wow. Really? They're making you jump through hoops for $12? Did the screen shots you took include the booking class or fare basis? If so did it match the booking class and fare basis of the ticket you purchased through Delta? That is the only reason I can think of that they might deny the claim as you met all the other requirements of their "Best Fare Guarantee":

Receive the difference in fare and a $100 travel voucher for use toward future travel with us.

The lower total fare found must be for exact same Delta flight, date, cabin, booking class (which begins with a letter such as L, U, T, B etc.) and flight time as the original itinerary purchased on the same day at delta.com, and the difference in total fare (including third party booking fees) must be equal to or greater than $10.

If you don't get any further through the regular channels I suggest you write a letter to Beth Reed. She is now in charge of the combined Delta/Northwest customer relations department but she was originally with Northwest which had a much better track record with handling customer care issues. Her mailing address is:

Beth Reed, Director - Customer Care and Refunds
Delta Airlines
1030 Delta Boulevard
Atlanta, GA 30320-6001