If a TV shows you something like 720p @ 60hz, it's telling you the source info, not what the panel is. All HD over the air in the US is either 720p or 1080i depending on the network and show. If you have a true 1080p TV, any signal below that is upconverted to the TVs native resolution and scan rate, if it didn't do that, you would be looking at a little 'window' in the center of your TV and it would never fill the screen.
You need to give us a make and model number. Actually with that info you could have confirmed yourself if the TV is indeed a 1080p set.
Even if the TV displays in the info bar that the feed is 1080p, it doesn't mean that it's really 1080p.
A DVD player that upconverts will show up at 1080p even though the source DVD is only 480i.