Thanks, himichel. Clearly, despite the manual, distortion control doesn't work on this G lens. (Same thing happens on my backup D5100, so it's definitely not the camera.)
With the kit 18-140mm lens, the Auto distortion control grays out and a message reads, "This option is not available at current settings or in the camera's current state." Seems odd, because 1) the camera is sold with this lens and 2) the function works just fine with my other lenses, including the 16-85, the 70-300, and the 35mm 1.8. Any suggestions as to why it won't work with the 18-140? My firmware seems to be up to date--C: 1.01 and L: 1.009.