PS3 1080p output problems.

I have a fairly new PS3 slim.  I just recently picked up a Samsung xl2370 computer monitor that supports HDCP and 1920×1080 resolution.  The problem is that for the life of me I can not get any game that I own that says it supports 1080p on the box to display 1080p on this monitor.  Modern Warfare 2 says it can do 1080p on the box, and in the display settings on my ps3 I’ve even unchecked everything but 1080p, and as soon as I load the game the whole system starts displaying in 720p or lower (not sure).  I bought this monitor so I didn’t have to stare at a pixelated, stretched, and  blurry mess that my 1680×1050 monitor created. 

Is there something else I need to do to get 1080p games to display in 1080p?  I’ve checked, and blu-rays are outputting in 1080p correctly.  They look amazing, but any game I play instantly lowers the resolution the ps3 is outputting. 

Any ideas?