In a word, "No". You can play SD discs in hi-def players, but not the other way around. Some discs are being released with the HD version of a movie on one side and the SD version on the other (so that people with SD hardware can buy now and watch the HD version when they upgrade their players and/or displays) Technically those are discs with HD content that can be played in SD players, but only the SD side will work.
I think somebody who heard that you can watch HD
broadcast (or cable) signals on regular TV with a convertor box has mixed that up with hi-def DVD.
Regards,
Joe