All three of those men were backed by the most powerful states of their day. Oppenheimer in particular is interesting because he headed up the most important,

All three of those men were backed by the most powerful states of their day. Oppenheimer in particular is interesting because he headed up the most important, but least expensive and labor intensive part of the project. He was also not the main project manager, he only managed the lab. Groves filled the role of the main project manager, and was not a physics expert. In fact his expertise was project management. Groves book emphasizes that his role was to delegate to the correct people, and use his influence to get things done. In other words it was PMs all the way down.