TBS shows "Seinfeld" in HD all the time - in 16x9, no less. According to wikipedia, they used the 35mm originals to restore image on the side while cropping the top and bottom.
That doesn't even make any sense.
If they went back to the 35mm originals, they wouldn't chop the tops and bottoms off the picture. The side material (chopped off for earlier 4x3 airings) would be there, and the picture would be fine for 16x9.
As a side point, it'd be odd if SG1 was "filmed in SD".
Old episodes of
Star Trek, on film, can be converted to HD. All it takes is recording the filmed material on HD video.
The "HD" was already there. Traditional TV just wasn't able to display the full quality of the filmed material, nor have even DVDs been able to.
Same would be true with SG1. The only problem might be special effects, but since even the gatesplash was originally done for a movie screen, that at least would exist in HD.
SyFy not running episodes in HD would be for the reasons already given-
They don't have HD copies of the episodes.
Similar thing happened when they wanted to run Babylon 5 in its widescreen format. The show had been filmed in a way that allowed for it to be shown in widescreen, but no copies had been made in U.S. TV format in widescreen.
They had to have a whole new set of films made up in letterboxed widescreen.
When things got up to season two, tho', someone at Warner messed up and instead of using the original films, they used the 4x3 copies and then cropped those to 16x9 and made letterboxed films out of those.
Fans picked up on what'd happened when they noticed people's chins and foreheads missing on closeups. (And some just plain recognized that the video was nothing but the 4x3 version with black bars on the top and bottom.)
If you want to see SG1 in HD, it'll have to wait until someone makes up copies for SyFy to run.