One of the guys with whom I corresponded theorized that it was the shaft vibrating against the inner part of the sleeve. He used a Dremel to grind just a bit off that part of the sleeve and eliminated the rattle.
That said, I've always been able to make it go away by tightening the set screw; sometimes filing the point makes better contact. Also, I picked up one of those plastic knobs with the 1/4x20 threaded bolt, available at most decent hardware stores, the type with an aisle of little drawers full of parts. I get plenty of leverage with the larger knob. It's worked for me on my Kay for the last 40 years.