His memory is correct, though it was earlier than he recalls, more like the 50s and 60s. The Motlow family didn't have enough capital to expand enough to meet demand, which led eventually to the sale to Brown-Forman. Demand was outstripping supply and they were on allocation, much as Maker's Mark is now, but I believe the situation for Daniel's was worse. The problem was simply the production cycle. Even when they were able to expand capacity, it still takes a minimum of four years to get additional bottles into the pipeline.
One solution was the creation of the Tennessee Squires. The strategy was to keep consumers loyal to the brand even if they were having trouble getting it, so they started this "club," with regular mailings and various free trinkets.