Well I agree myth 1 and myth 2 are absolutely false. History has always had a problem with defining itself from public memory. Stop people on the street and they will say - yes the bomb stopped the war. Read history and you find it was the Russian invasion.
Myth 3 is a little harder because he does not define what he means by war, or what sort of war the bomb was meant to stop. Small bush wars and proxy wars were always going to be fought, that was the point of the founding of the UN. It is total war like we saw in WW1 and WW2 the bomb was tasked with stopping, and we have to agree it worled.
Myth 4 - see my comments on myth 3
Myth 5 - I confess I can not figure out what he is talking about.