While I concur with what the policy states, in practice, the companion has their own boarding pass. On the boarding pass, I do not recall a designation of a companion. Thus the TSA doesn't know, and the gate agent also doesnt know. Obviously the computer knows...but if I had missed my flight I wonder if they would have pulled the companion off the flight?
Not trying to game the system, was a real situation that could happen if you and your companion get to the airport at different times.