I'm a controller, not a pilot.
It would seem to me that the captain was the victim of one of several human processing errors referred to as confirmation bias.
When asked by one of his crewmembers if the PanAm flight was clear of the runway, he replied with certainty.
Nobody, no matter how arrogant, would take off in fog knowing (or even suspecting) that the runway wasn't clear.
As you're probably well aware, there were several contributing factors, including jammed or blocked transmissions as the crew performed their final departure checks.