Had a similar problem
I realize this is an old thread, but this information may prove useful to others.
My '03 was making the same groaning sounds on start-up. I took it to the dealer for the service interval that was almost due and they told me the release mechanism was rusted, causing the rear brakes to drag.
They then went on to tell me that the rear brake rotors (at 45K miles) were so rusted that they would have to be cut off the truck. Estimated cost was $750. The dealer also said that this was a fairly common problem with the F150 and that Ford had redesigned the actuator to eliminate the problem.
Keep in mind that just 3,000 miles before, they inspected the brakes and said they were all in good shape. Since I needed the truck to be fixed, I let them do the repair, then wrote a letter to William Clay Ford after the Customer Assistance Center told me there was nothing they could do to help. After a few phone calls between the dealer, Fords office, and myself, Ford reimbursed me for half the cost of the repair.
I'd be curious to know if any of the other members here have encountered a similar issue.