It appears to be the interference as Old1625 described it. I can move the DTV box around, limited by its two-foot coax cable (supplied) and find a "null point" where the interference has little effect. Moving it farther from the TV in general diminishes it. It's obviously coming from the converter.
The Digitalstream from Radio shack does the same thing.
Something to think about when designing your DTV-to-Vintage setup. Maybe the Zenith is particularly suceptible (or somewhat misaligned). I'm curious how others fare with this.