That's a terrific anecdote and piece of important family history that underlines the point made in the film. Both perspectives on dropping the bomb - including that it would mean US troops coming home instead of being embroiled in a bloodbath that could potentially cost more lives - are discussed and pointed out. The audience is left to draw their own conclusions about the legacy of that decision. Also, the film makes very clear that it was indeed Truman's decision, though Oppenheimer is still plagued by guilt.