I think it is safe to say there was some "poetic licence" in the documentary. As TURIN rightly points out the original 747 design came from a military requirement, which was to be fulfilled by the C-5A. However Pan Am was instrumental in Boeing developing the 747 as a passenger aircraft and highly influenced the design. Arguably had they not done so, then the 747 may not have come about, or at least not as soon as it did.
As for the Comet, I guess we should be grateful it got a mention. Sadly its early problems played in to the hands of Boeing (and Douglas) who produced true transatlantic capable aircraft that DH could simply not compete with.