I will ask this again. True or false, do I need a monitor if I want to play a game at maximum resolution (assuming the game exceeds 1080p). Say I want to run ARMA 3 at 2560x1600, are you telling us that I can do that just fine on our 60" Vizio LED at 2560x1600?
Do you have the option of playing at higher than 1080p on consoles? No. If they did would you need to buy a new TV? Yes.
PC games render natively at whever res you set them to, unlike consoles.
All once again, based on ignorance.