wikipedia is a continuously updated web encyclopedia, and as such its accuracy is a sort of "accuracy of the majority." As far as Einstein and Szilard are concerned, neither was directly involved in the bomb development and the decision to use it. Szilard has been credited with the basic conception of nuclear fission, and he wrote a letter for Einstein to sign to 'get the ball rolling' in 1939, I think, when it appeared that Germany might have a technical lead in bomb R & D. Neither of them actually participated in bomb development. That means that neither would be a part of the decision making process. There were, of course, many scientists who were in favor of using the bomb, including, at the critical moment, J. Robert Oppenheimer, the technical and scientific leader of bomb development at Los Alamos.
An important correction to the above post that Truman had two bombs. There was a third bomb released to the military. After the bombing of Nagasaki, the American leadership mandated the return of the bomb, a 'fat man' plutonium bomb identical to the Nagasaki bomb, back to civilian control. Obviously, it was never used.
The tempest over whether WWII was a nuclear war or not is moot. It is certainly spurious to maintain that there was a four day 'nuclear war' within the greater conflagration of World War II. At the time of first use, atomic weapons were merely considered new weapons, such as poison gas of WWI. It was from the people closest to the new developments that the argument came to consider these weapons of a new class altogether. These people knew something that no one else knew, that waiting in the wings was the potential development of a 'new' new bomb, 1000 times more powerful than the atomic bomb. When this concept was first tested, it eliminated the island it was mounted on.