That's far from the complete truth. The unsaid fact is that Mosaddegh was trying to nationalize British and American owned oil operations, which was what prompted our actions.
Ironically, Shah was a very modernizing influence in terms of rights for women and minorities. Yes, the man was batshit crazy, but he was aimed to create a secular state. Unfortunately, when the people revolted against him, Khomenei and his Islamic fundamentalist ilk essentially stole the revolution from the left liberals and established a theocracy in its place.
Much like what's happening in Egypt today, where the Islamists have taken over a revolution from the left liberals.
So, blaming the US for part of it is fair, but this is a classic example of unintended consequences.