What films are you referring to? Your note about them having no military training perhaps betrays a bit of an assumption you may have about the CIA that may need some correction.

First, the CIA traces its lineage from the OSS, which was organized to coordinate intelligence gathering for the Joint Chiefs of Staff during WWII. During the war, the OSS had its hands in not just intelligence gathering but also some activities that are more in the realm of special operations today (recruiting, training, and supporting irregular forces). However, by the time the CIA was created by the National Security Act of 1947, the OSS has been dissolved for a few years and its military functions were not really preserved in the CIA (they would come back later). At first, the CIA's function was mostly analysis, as it did not have a significant intelligence gathering capability. In that light it makes sense that the agency would be staffed with well educated folks. Even as the CIA grew in its intelligence gathering or "operations" side, operations officers only rarely had jobs where military experience or excellence was important or even helpful.

I can't answer this question fully, but I highly recommend you read Charlie Wilson's War, which was made into a decent movie starring Tom Hanks, Julia Roberts, and Philip Seymour Hoffman. The movie doesn't examine this issue much, but one main theme in the book is Gust Avrakotos' improbable ascension in the CIA and the difficulty he had gaining the respect and trust of his colleagues and superiors in the agency.

You see, unlike his contemporaries in the CIA, he was the son of a blue collar, immigrant family. To answer your question: In general, yes, the CIA was initially composed of the wealthy elite who had political connections. However, the CIA realized it needed to tap into the country's vast network of immigrants in order to conduct many of its operations overseas. So in the late 1950s/early 1960s the CIA began a campaign of recruiting highly gifted and qualified second and third generation immigrants to go back to their native countries to act as agents. Gust was one such agent and he found himself back in Greece on his first assignment after being recruited by the CIA.

Anyway, from what I remember in the book, there was a huge divide in the agency between the established elites and the newly recruited agents who were either immigrants or the children of immigrants. Obviously, they were under a lot of suspicion (fears of them being double agents and such), and in general it was much harder for them to advance in the ranks. Often they were given the more dangerous assignments, and some would argue that the upper brass even treated them as expendable.

Not sure if that answers your question, but it's an interesting facet of the agency's history during the Cold War.