Note that his thinking didn't turn militant until he was jailed and tortured by the Egyptian government. That at the time had backing of USA, and thus trained by the CIA.
Yes, and this is vital. Thank you for mentioning this. A lot of radicalization occurs for a reason. People don't just stumble across radical outlets and casually indoctrinate themselves. They are catalyzed first.
His Wikipedia article disagrees with this, saying "Upset that Nasser would not enforce a government based on Islamic ideology, Qutb and other Brotherhood members orchestrated a plot to assassinate the Egyptian president in 1954. The attempt was foiled and Qutb was jailed soon afterwards;"
I guess someone will have to take that up with Adam Curtis...