Shutter in right rear

I have a 2007 ford F150, purchased used. I noticed a slight virbration in the right rear tire/wheel area and it is there mostly at low speeds and more noticeable with a load on the truck, such as a trailer. I took it to Ford and there is a TB about this problem and they shimmed the rear axle at the shackles and it is still there. They had the vehicle several days and did not charge me, and said it was typical of that year of ford pickups. The truck has a 3:55 gear ratio and a slip differencial. I have not idea of what this could be and thought I would submit this to car talk.