I photographed that sign on the Northbound side of the Natchez Trace Pkwy at the Hwy 100 Bridge just at the North End terminus (close to Loveless Cafe).
There is no official parking at that end, however, there is an official parking lot on the other end of the bridge (Southbound side) with pedestrian access to the bridge. (Whether pedestrians are legally allowed on the bridge or not, I do not know, however it is easier to do so from the North end, and I have seen hundreds of people do so to take photos)
There is NOT a "No Drone" sign on the North end (Southbound side) where the parking lot is, only on the other end. So..........I take that to mean that they do not want people parking on the road shoulder and entering the bridge via foot from the South end, especially to fly a drone. From the North end....there is a significant sized parking lot, perhaps "less danger".... But... no sign.
Forgiveness...Permission...Blah, Blah, Blah....
The way I see it, if you enter from Hwy 100 (the Northern terminus for Natchez Trace Pkwy), and immediately park in the "overlook" lot, and then proceed to do whatever it is that tourists do there, you will never have opportunity to see the backside of a small sign that is over 1,200 feet away on the other end of the bridge and does not necessarily pertain to whatever it is that people do on the opposite end.