I've read narratives attributing it to the US and UK in serious sources, such as (IIRC) Foreign Affairs.
- The clerics were the most powerful political group in Iran, and were the best organized. The main enemy of the clerics were the communists.
- The communists were making headways, which made the clerics extremely unhappy
- Mosaddegh was viewed as appeasing the communists, which made the clerics even more unhappy
- Mosaddegh rigged a constitutional election (99% votes to agree) which made him extremely unpopular
- The initial US-Anglo coup efforts actually failed
- The UK had financial interests, assets on the ground, and much more experience with coup plotting than the U.S.
- The US didn't have a lot of assets on the ground or particularly understood Iran very well, given that this was shortly after WW2 and they were just starting their world-policing role -- rather incompetently.
So that would be the starting point for skepticism about the importance of the U.S. role, which just comes from background knowledge.
Note I am not saying the U.S. was not involved in making payments. It was. I am saying that that was a secondary role.
Now, onto specific data. It is based on the following observations:
Whereas US FRUS data attributes a huge role for the U.S., British data does not. And the British were much more involved in Iran. So how can that be? Well, the theory is the US CIA station chief exaggerated his role, and then this went into FRUS and right into the eager hands of all the Chomsky readers out there who want to view every nation as without agency, without internal political forces, but merely as puppets of the U.S. which can snap it's fingers and force regime change wherever and whenever it wants.
Here is a link to an article covering some recently declassified British data:
"In recent years, new interpretations of the coup have called into question the accuracy of various U.S. archival records and first-person accounts, discounting the importance of the CIA and British intelligence role in the operation and casting doubt on any connection between Iranian clerics and the Western powers. The principal aim of the latter contention is to bolster the case that Iranians, including leading mullahs, acted essentially (if not entirely) on their own in bringing about Mosaddeq’s ouster."[1]
Here is more data from Foreign Affairs[2]:
"Yet there was a supreme irony to Obama’s concession. The history of the U.S. role in Iran’s 1953 coup may be “well known,” as the president declared in his speech, but it is not well founded. On the contrary, it rests heavily on two related myths: that machinations by the CIA were the most important factor in Mosaddeq’s downfall and that Iran’s brief democratic interlude was spoiled primarily by American and British meddling. For decades, historians, journalists, and pundits have promoted these myths, injecting them not just into the political discourse but also into popular culture[...] That version of events has also been promoted by Iran’s theocratic leaders, who have exploited it to stoke anti-Americanism and to obscure the fact that the clergy itself played a major role in toppling Mosaddeq.
In reality, the CIA’s impact on the events of 1953 was ultimately insignificant. Regardless of anything the United States did or did not do, Mosaddeq was bound to fall and the shah was bound to retain his throne and expand his power. Yet the narrative of American culpability has become so entrenched that it now shapes how many Americans understand the history of U.S.-Iranian relations and influences how American leaders think about Iran."
You can read the rest of the FA piece if you have a subscription. I put the text into a pastebin here: https://pastebin.com/WeL21Ss5
But if you are interested in foreign affairs, I recommend a subscription.
----
[1] https://nsarchive.gwu.edu/briefing-book/iran/2018-03-07/new-... see also https://pastebin.com/WeL21Ss5 for free copy
[2] https://www.foreignaffairs.com/articles/middle-east/2014-06-...
The US (and UK) could play significant or necessary roles, without playing the leading or primary roles. And of course defining primary role is complicated: Is it influence? Power? If person A bribes a head of state to enact a certain policy, who has the primary role? The head of state does most of the work and has most of the power, but the briber was most necessary to it. And it would never happen if other parties and circumstances didn't allow it. Back to Iran: Of course there were forces opposing Mosaddeq that the US/UK backed: There are always other forces, though of varying influence, and how else would the US/UK do it? They weren't going to invade with their own troops. Only a complete moron (or George W. Bush, Dick Cheney, and Don Rumsfeld, with help from Tony Blair) would topple a national power structure without another power structure to replace it.
Also, having read a lot of foreign policy, I would say that few Americans know the narrative of overthrowing Mosaddeq, and fewer believe it. I'd guess almost the entire right wing of the political spectrum disbelieves it, as do most centrists.
Which isn't to say I know the real story. I imagine there is a lot of nuance, and framing it around the amount of influence the US/UK had compared to the clerical parties seems misguided - it's not a competition, and it gets us into matters of definition (as discussed above). Perhaps my feelings would be different if I was Iranian. I do get that Western foreign policy tended to objectify everyone else.
-------
I read those Foreign Affairs articles at the time (there were several, about Iran, Chile, Congo/Zaire, and I think elsewhere). My memory: While they were valuable for their perspective and arguments, some were quite improbable. IIRC Zaire and Chile claimed ignorance of what was happening and naivete about the intentions of the dictators. I don't recall what I thought of the Iran article.
So, maybe they had nothing to do with it and just lied about it, but your claim that they didn't even know how to do that kind of thing is plainly false, which throws doubt on the rest of your claims.