Looking back on it the idea of a successful preemptive strike seemed laughable and the idea of the government actually trying to pull it off seemed divorced from reality.
Only if you weren't from OUR reality. A
preemptive first-strike was considered a best-option-amongst-bad-options kind of issue. MAD,
Mutually Assured Destruction, was the policy of the day. The idea was that pulling the trigger kills us both...and knowing that prevents anyone from pulling the trigger. Which led to the cold war, where the two super-powers would fight by proxy in places like Afghanistan and Nicaragua. A pre-emptive strike presupposed that maybe...MAYBE...you could do enough damage to your enemy before they had a chance to damage you and thereby limit their capacity. For varying values of 'success' in this case, which would be, losing tens of millions instead of hundreds of millions. MAYBE.
I'm just saying that no matter how strongly he felt that way the world he portrayed was more divorced from reality than he probably realized.
As others have already pointed out, the world he portrayed was much closer to the mark than you know. Links are provided above, but seriously...we have come close to nuclear conflict several times, particularly in the heated atmosphere of 1983, when we came damned close. Moore may have turned up the rhetoric a might, but the danger and threat in the real world were very real.
There was propaganda everywhere trying to sway people politically and not a whole lot of information resources available to the general public.
We DID have ways of passing information around before the Internet that didn't involve depending on what we saw on Television, you know.

Sometimes the information channels were slower or clumsier or uglier to look at, but there were plenty outlets and venues for that information to be circulated. Trust the folks who actually lived through it...we weren't blind puppets to some propaganda machine. Ronald Reagan and Margaret Thatcher were just as heavily criticized as any other US or UK leaders (which is to say,
heavily).
Of the many criticisms that one could levy against the Watchmen, the fear of a full-scale nuclear war being apocryphal is not one of them.