Okay, did some testing and here's what I found out.
I first took a different, random video clip and that indeed did reverse properly. Then I tried to reverse the video I was originally working with, and that still will not reverse.
Here are the specific circumstances: I have a video clip showing a flyover of three different cities. I trimmed out the third segment and wanted to reverse that, so it was flying toward the camera instead of away from it. I have a text overlay, typewriter, displaying the city names along with audio clips down in the audio track for the typewriter sound.
Opening that project, then separating out the third segment will not let me reverse it. However, I deleted everything from the project except the video clip, then it will reverse. I ended up just exporting that to its own separate video file and then importing it back into the project.
Is that just weird, or was I violating some "reverse clip" rule?