Are we sure that the original film stock is 4:3? These were posted a while ago (thanks StewMc) but here is an original shot from Menage a Troi:
Then how the same clip appeared in widescreen for "These Are the Voyages":
It appears that there is at least some information in the picture beyond what made it to the videotape.
Maybe it was filmed in 16:9 then cropped to 4:3 for the video? (Yes, I'm being optimistic)