https://en.wikipedia.org/wiki/1953_Iranian_coup_d%27état has a different story.

See also the manner in which "the" Shah inherited his job from his father: https://en.wikipedia.org/wiki/Reza_Shah#World_War_II_and_for...

Yes, ruler of the country may be arguable. I note that Churchill, not Elizabeth, is held responsible for the UK's actions.

https://nsarchive2.gwu.edu/NSAEBB/NSAEBB435/