Great list of references. I say keep, "U.S. Backed" in the lede. As to the main point (not the language usage point), I am actually amazed that we are having this discussion.  I have never seen any reputable source that does not call him "a U.S. backed" leader (or words to that effect). While it is true that the exact nature of Batista's relationship with the US was complex and varied over time, all major sources inside the US, inside Cuba and as far as I know through out the world, describe him as being "US Backed - from shortly after the coup in 1933 until shortly before his fall from power.  The body of the article can, and does, detail the nuances of this relationship, but the lead is meant to give a broad summary of the topic.  Using "US Backed" is the best way to do this.  As to Kaisershatner's linguistic point, to me "U.S. Backed military leader etc" is shorter and more to the point that is "military leader backed by the Untied States."