Did Truman really decide to drop the bomb?

During a visit to the Truman Library and Museum, I noticed a small quote on the wall that said the military had already decided they wanted to drop the atomic bombs on Japan, and Truman just went along with it. He simply didn’t interfere with the military decision making. Truman didn’t even learn about the Manhattan Project until a week or two after he became president, so it is believable he didn’t fully understand what the bomb was and was capable of.
Was it not until later in his presidency that he started to claim that he had been the one to decide? Did Truman re-write his contribution to this part of the war?