I run into this at work sometimes, only in my case I get a heavy pink shading when I hook some units up to my test monitor. So, working on the assumption it's a case of you hitting that very narrow error buffer on digital connections, try wiggling the cables and the adapter a little. Don't get too violent or anything, just make sure all the connections are secure, maybe even pull them all out, reattach them. Also make sure that the cable isn't being bent considerably.
Also, you might try looking around for any other games that only play at 720p, and see if you can find them at some video rental place. Then you can find out if it's some issue with the TV displaying 720p images. Which seems a bit unlikely, but definitely something you'd want to rule out. If it's the TV, no amount of fiddling with cables will do any good. You could also try taking the game back, getting a different copy. There's a remote chance there's a defect with that particular game disc.
I have a PS3 Slim that is setup with HDMI->DVI connection to a Pioneer 5070 plasma display. It has worked great for BDs at 1080i/p and DVDs as well. I recently bought a PS3 Game that plays at 720p (ModNation Racers). HOWEVER, the display for this game does not work properly - the screen turns GREEN as the game starts and most of the visuals of the game retain a green color (up to 80% of the images on the screen). Tried playing the game for some time, but the green color remains.Have tried changing the PS3 Video Settings, but not been able to fix the problem so far. Would really appreciate some help in resolving this issue - my 7 year old son is giving me a tough time since his game is not working ! Thanks in advance.