I hear rumors all the time about different companies. One of the most persistent is that Jack Daniel's doesn't go through a second distillation. I was there earlier this week and specifically asked to see the doubler. I saw all of them. They have five doublers, one for each still. They are conventional doublers, not thumpers.
Yes, they have five beer stills. Stills 1 through 4 look like any other distillery's column still. No. 5 is the same except twice as big (in diameter, that is). Happily, they were shut down while I was there. It must get miserably hot there in the summer.