I used to agree with them. Then I saw Fail-Safe.
Also shot in 1964. Also about the cold war. Not a satire, but a riveting drama that haunts you for days afterwards. It died at the box office because Stanley Kubric found out about it and insisted his movie be released first. A serious movie released after a satire on the same subject does not make a box office smash.
The two books upon which the movies are based, Red Alert (which became Dr. Strangelove) and Fail-Safe are nearly identical. So much so that the writer of Red Alert sued the writers of Fail-Safe for plagerism. It was settled out of court.
Despite that dubious honour, Fail-Safe is an incredible film. Directed by Sidney Lumet (12 Angry Men), the use of lighting, close-ups, and silence drive the tension in this film sky-high. And the ending will leave you shocked.
If you like, you can see it on Google Video, but you'll have to watch it in pieces. I say, rent it or find it, and watch it all the way through. It's incredible.
Here's the opening: