"Backing" usually implies more than words.

Most of the world's countries during the Cold War were newly formed and generally not very democratic - while the US did overthrow several democratically elected governments - Mossadegh's in Iran; Arbenz in Guatemala and Goulart in Brazil - the vast majority of situations were of the US choosing to back already-established strongmen and factions, backing new strongmen and factions against old strongmen, or else offering their support to such autocrats who were 'feeling out' the offers of the US and USSR.

While the CIA has a reputation for having their grubby hands in every pot, the fact of the matter is that even with Cold War era funding, the CIA had limited resources with which to perform their misdeeds, and often very limited intel. Reading Cold War histories, one is shocked by how commonly the CIA is caught off-guard by some coup or change in orientation - because they're pouring their resources into trying to assassinate Castro for the millionth time, or fucking up a coup elsewhere and ignoring the reports from the local US embassy.