1999 Chevy Tahoe, 5.7 liter, 100,400 miles - vibration

Recently, I had a complete brake replacement done on my Tahoe. The mechanic replaced front rotors with brand new ones, and new pads. In the rear, they replaced the brake drums, but not the shoes, as those were determined to be in good condition. Immedietly after doing this, I noticed a very violent vibration at speeds from 65-80 miles per hour. The body, seats, and dash board vibrate and shake, but the steering wheel tracks straight with no vibration. Braking is smooth. The tires have been balanced by a reputable tire dealer 2 times, and a front end alignment has been done. The shock absorbers are nearly new. The mechanic has told me that there is no way that the vibration could be coming from the brakes, and that my tires must be bad. But, the tire dealer assures me that my tires are perfect. Is it possible that one of the new brake drums is not properly balanced? Or, could the vibration be the result of not replacing the brake shoes?