Actually it was Captain John Collins (not Rob); former BEA Trident co-pilot who moved onto Vanguards for his command. I totally agree with you; John Collins was positioned directly behind Captain Key and there was a rumour that he recognised what had gone wrong un-buckled his harness in an attempt to re-select the droops as his body was found by a fireman across the centre console and his head set by Keighley's rudder pedals. Like all the theories, we will never know for sure what went on.
Its a shame that National Geographic got it wrong; I think the Papa India story needs a good 1h30mn to tell all of the facts.
I also noticed that they got the uniforms slightly wrong (no wings were worn on the shirts) and the rank of Keighley was SFO (three stripes) when in fact he was a junior FO; so would have had two stripes. SFO Ticehurst should have worn three I believe?
Even the R/T messages were not quite correct and they also omitted the fact that Papa India informed LHR ATC that 'they had a small problem' before lining up on 28R for take off. The small problem was not established and the delay was only a few minutes before they reported ready for departure.
Finally and I could go on for hours; the programme omitted the fact that all three engines were running and Papa India was about to push back off stand when the BEA Dispatcher appeared on the flight deck to say that the Vanguard crew (Captain Collins) were required in BRU and would somehow have to be accommodated. This required off loading of some cargo, re-issuing of the load-sheet and a further delay; adding I guess to Key's stress.