I think that for the US to have beaten the Soviets in placing a man in space, you would have to go further back in time than simply the Ham and Able launches. The Soviets were well ahead of the US primarily due to one man: Korolev. It was his development of the R-7 rocket that accomplished everything. But in April 1957, there was a mishap - an R-7 prototype exploded. Had that (and I do stress here, HAD THAT) been as devastating an explosion as that of the N1 explosion of 1969 and killed Korolev then it is possible that Khrushchev would have lost interest in the ballistic missile program and scrapped it. That would have given the US - which was far more concerned with nuclear capable bombers - time to catch up and potentially surpass the advancements of the Soviets. Eventually, I think, Van Braun would have been given a chance to pull off a stunt like Korolev did and put a satellite into orbit. That being the case, it would have been the Soviets playing catch-up, not the US. It's entirely likely then that the US would have beaten the Soviets to the punch and placed a man into space first.
But that's a lot of "ifs," and it is not how history actually turned out. This is just "navel-gazing" and I'm honestly surprised that something like this would turn up on Yahoo News (not that it's the greatest source of news in the world, but still). I think it's time we started looking forward, not backward - at least in terms of space exploration.