I think that’s the lamest scenario I’ve read yet. It assumes that two pilots could not utter a simple phase: Ground control, smoke in the cockpit. Pilots can speak and do other tasks simultaneously.
Actually, this is very plausible. Pilots only talk when they have time. Smoke in the flight deck requires O2 masks. Talking to ATC is the least of your worries. Sometimes 5 or 10 minutes after an emergency procedure. ValueJet cargo fire gave the crew only minutes to response time.