Anyone know why this game refuses to run in anything higher than 720p even though it supports higher than that? GT5

and Call of Duty both run in 1080i on my tv. (32 inch sharp)
I think you'll find the answer(s) you are looking for just a few posts above yours (
#2105)
To sum it up, neither COD4&5 nor GTAIV are rendered natively in 1080p. Only GT5P is. In addition they are certainly not rendered in 1080i. All current games are rendered natively in progressive format. If you choose to you can set the PS3 to convert the signal to a 1080i, but that is not native.
It's extremely important to understand the difference between rendered and scaled resolution, progressive and interlaced video, and native and supported resolution.
Based on your comments and questions I think you have several of those confused with the other.
Depending on the type of display you have, just because it says it "supports 1080i" doesn't at al mean it can actually display a 1080i signal. If it's a fixed panel display (LCD, DLP, PDP, LCoS, OLED, etc) then it has a fixed pixel panel (native resolution). If it is a 720p/768p panel, then even though it "supports 1080i", all it is doing is taking that signal and downscaling the image to the native resolution of the display. Not only that, but because they all are progressive displays, they also have to deinterlace the 1080i signal. All of this is a quick way to lower the quality of the original 720p source.
So unless you have and analog TV (CRT), or if you don't have a 1080p TV, then you should make every effort to avoid feeding your TV a 1080i signal. I realize this is not always possible, as many HD broadcasts are only available in 1080i, but at least in terms of the two games you mentioned, GTAIV and COD, then by all means you should not be forcing your PS3 to upscale to 1080i or even 1080p.