How come games say they're 1080p when even with the right tv and cable its only 720p?

I have been playing the Assassins Creed series. I have already beat both games with Ezio. On the back it says that best graphics are 1080p. My hdtv is full 1080p. My ps3's opening screen is 1080p but whenever im playing a game ill switch from hdmi 1 to hdmi 2 and back aand its says its only 780p. I was wondering if its because its a multiplatform game if it does support 1080p how do i fix it?