The crew was never in contact with the tower controller that was in a position to see that gear were not down, or that the aircraft had landed on its engines.

The crew was never in contact with the tower controller that was in a position to see that gear were not down, or that the aircraft had landed on its engines. For reasons that are not clearly explained (probably everything happening too fast and muddled), they remained in contact with approach during the landing after the approach controller got their landing clearance from tower on the phone. Tower did report the gear-up landing to approach, but approach did not relay to the crew.