Well, Adam Curtis borrowed far too much from Straussian critics like Shadia Drury to come to that conclusion. Irving had always stated that he never really felt comfortable belonging to one group or another throughout his youth and adulthood, hence the "neo" designations he famously joked about so often.
Strauss did have a profound impact upon him, but so did Lionel Trilling and many others (include fellow Partisan Review members, fellow Alcov 1 classmates, early supply side economics proponents, fellow Public Interest writers, etc). Irving Kristol was the product of many intellectuals, family members, Jewish culture, and his own natural intuitions. This is why he stresses that neoconservatism is not a doctrine, a dogma, but rather a impulse.
You really get a sense of that by reading his writing. That is why I have this real distaste towards Adam Curtis' documentary, no matter how many times I see it. He simply looks at the Straussian angle in the wrong way and presupposes that it essentially is neoconservatism rather than one wing of an incredibly complex label. I mean, if you think about it carefully, everything Curtis does with that documentary (besides grabbing content from copyrighted sources without really communicating enough with said copyright holders, thus making it difficult to ship his content through mainstream vendors) is to create this really nice and clean narrative about how to seemingly extreme characteristics of international relations are confusing the reality of the human existence, and that everything should be just fine if we simply accept that these leaders are shaping us towards a paranoid existence and we deny their premises. If you start to spend time examining one person in the theory, and expand outward, his whole documentary seemingly falls apart.
I spent my time focusing on the neoconservative front, and bit by bit, I discovered how Curtis really just put together a shoddy product of others' work and once I examined the originators of that interpretation, you could find countless amounts of holes. But, you know, it's on the internet, it's spread quickly, it's promoted by the BBC, it has fantastic music, impressive visuals (again, taken from other sources), and has a fantastic narrative, but it's a really poorly examined thesis when you get down to it.