I would think that this is just a rumor.
The nuclear plants on the reservoir have to have intake water for cooling purposes, after a 12 foot drop that would decrease the water available for the plants. If the intakes were even under water at those levels (not sure I know that they were extended several years ago, but not sure how much). I would think that we would have heard about this due to environmental concerns.
Also, what affect would reducing Chickamauga by 12 feet have on the area below the dam? None -- the levels would be the same below the dam where the new lock is goin in. Reducing the levels on Nick-A-Jack would make more sense. But, they have a weir dam around the new lock. So why would the levels need to be decreased??
And as stated above, no one would have access to the lake. No ramps would be available for launching. The boats at the marinas would be on dry land as some of the marinas would be dry. And last, how would the river traffic for barges be handled? Not much room for error when their navigation.