You are wrong. TCAS has nothing to do with radar. It is on board equipment that actively interrogates transponders in nearby aircraft and displays their position relative to the airplane equipped with TCAS. It cannot see airplanes without transponders, or planes that have the transponder turned off.
We call devices that determine range and direction by interrogating other aircraft's transponders secondary radar. It's perhaps not the best term but it is RADAR.
It only works if the guy is presenting mode C by the way. A transponder itself isn't sufficient.