TV screen in still photo: Why are there dark, blackish bands?
Yes, you're basically on the right track. The bands appear because the camera shutter is not synchronized to the vertical scanning of the CRT.

A fast shutter speed will only capture part of a scan. A shutter speed exactly equal to the vertical scan period will capture a full scan, but there still might be a narrow band (either dark or light) somewhere in the image if there's any mismatch in the timing.

To minimize the banding, use a shutter speed that spans several vertical scans, but this only works if the image on the CRT is static.