One problem with the theory: The first communication system was shut down before the pilot's last message 'All right, good night'.
If it had been an accidental fire that caused the pilot to cycle the systems, I would imagine the last message would have been more along the lines of "Holy Smokey Bear, the plane's on fire!"
The NYT is saying that some Malaysian government officials are confused about how ACARS works, leading to the confused reporting.
The above comment is accurate: the last ACARS message was received at 107, and the next one was expected at 137. The voice communication was logged at 119.