I spent 35 years flying fighters, and you can see the guidance system kick in...The first assertion is meaningless unless he spent those 35 years flying fighters while observing ballistic missile launches.
And the guidance system in those suckers is running in the launching tube or silo. It doesn't 'kick in'. I suspect he's thinking about the old SA-2 system we flew against in Vietnam, which followed a pre-programed launch trajectory until the booster dropped off, exposing the guidance antennas.
I wouldn't be so quick to claim that no SLBM (or even a barge-launched missile) of any kind, made by any nation, "kicks in" or otherwise makes course corrections of the kind shown in the film. There may be some analysts who possess such knowledge, but I would imagine there aren't many.