If you're holding out for a hero, Bonnie Tyler, I'm not the guy.

I can't tell you just what you're talking about without hearing it myslef. I was afraid you might give the answer you did, because it obviously can't help to narrow it down other than to say it apparently is not a specific station or TV.
You mentioned multi-pathing, which was one thing I thought of if it was analog broadcast TV (though typically that will affect the video at least as much or more than just the the audio).
Other options that come to mind (just shooting in the dark here):
- Bad/worn videotape of the re-runs at the stations causing some flutter on the audio track.
- Some poor mix of false stereo played through a mono or close-stereo TV playback, or a mono signal being false stereo-ized by a decoder in a stereo TV.
- Too much Johnny Walker Red (either at the station or in your home, or both)

.
G.