The CIA was a just born organisation and Ajax was the first big operation. The CIA, to gain a good profile had to inflate it's role and influence to impress upon Eisenhower.
Kermit Roosevelt, the head of the CIA operation, was notoriously exaggerating his involvement in the coup in his account of the events. Some of that stuff is downright ridiculous and factually wrong (like Roosevelt supposedly riding on the tank conquering Mosaddeq's house...). The CIA report is choke full of self-serving revisionism and possibly partly plagiarized of an Persian article based on an interview with Ardeshir Zahedi, the son of Prime Minister General Zahedi and later Ambassador to the US, both central parts of the coup to reinstall the Shah.
Eisenhower himself voiced his disbelief over the reliability of the CIA account of events. In the word's of Ike the CIA account read more like a "dime novel" than fact (writes so in his diary).
The young CIA had to prove it's worth and mettle to the US government. Exaggerating it's role in Iran, and deminishing the role of Iranians and the Shah, was transparently part of that effort.
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iow, believe SW instead of an actual de-classified document written by the men who were there. I think not.