I looked up 36 CFR § 261.18 which the sign cites as the legal authority behind the prohibition. This purports to ban the possession of "motorized equipment" in wilderness areas. According to the same chapter in the regulations, "motorized equipment" is defined as:
So the law itself seems to exclude smaller battery powered devices, and even gives cameras as an example. I wonder if anyone who has received a ticket under that regulation has argued that the posession of a drone could fit into that exception as well. Something like a Mavic Air isn't really larger than a full frame DSLR camera, has photography as one of its main functions, and is also battery powered.
That said, it's probably better to not tempt fate and avoid getting the ticket in the first place.
But they cited 36 CFR § 261.18 (a)(c) and when you look at (c) it pretty well locks it down
(c) Landing of aircraft, or dropping or picking up of any material, supplies, or person by means of aircraft, including a helicopter.
I know someone is going to say, "But it doesn't restrict Taking Off" (rolls my eyes preemptively LOL)