How BBC World Service was used by Churchill in 1953 coup in Iran

BBC World Service is celebrating its 75th anniversary. They must be happy about such achievement and they deserve to.

But for the rest of world two aspects of its operations, at least, are very problematic:

a) That its funding is entirely coming from The Foreign and Commonwealth Office, and therefore it affects the perception of its editorial independence among the audiences

b) That history shows how such close ties with the government has actually produced embarrassing moments. The best example for that could be the BBC's role in relation to the CIA-MI6-engineered coup against the Iranian prime minister, Mohamad Mossadegh, in 1953 which is documented in Stephen Kinzer's book, All the Shah's Men:

Roosevelt told the Shah that he was in Iran on behalf of the American and British secret services, and that this would be confirmed by a code word the Shah would be able to hear on the BBC the next night.

Churchill had arranged that the BBC would end its broadcast day by saying not "It is now midnight," as usual, but "It is now exactly midnight." Such assurances were hardly necessary, the Shah replied. (p. 9-10)

Don't you think this would make the whole population of Iran always suspicious of the BBC's journalism?