That justification was made after the fact. The truth is that Japan was already going to surrender. This isn't a conspiracy theory either, it's modern historical consensus, even the US Navy's museum admits so. The USSR had just taken Berlin and the Nazis surrendered on May 8, and declared war on Imperial Japan on August 8 after both Japan and the US had seen the Red Army pivoting to their East, towards Manchuria.

On August 9th, the Soviets invaded Japanese-controlled Manchuria, and Japan announced surrender on August 15th. The nukes were launched on the 6th and 9th of August, because the US didn't want Japan to go Soviet, the US had plans of reforming Imperial Japan as a subsidiary Empire, maintaining Japan's colonization of Korea and other Asian countries while profiting off of Japan, in a form of double Imperialism, and a Soviet Japan wouldn't let that work. Their plan was thrown to dust with the Korean War that followed.

While publicly stating their intent to fight on to the bitter end, Japan's leaders (the Supreme Council for the Direction of the War, also known as the "Big Six") were privately making entreaties to the publicly neutral Soviet Union to mediate peace on terms more favorable to the Japanese. While maintaining a sufficient level of diplomatic engagement with the Japanese to give them the impression they might be willing to mediate, the Soviets were covertly preparing to attack Japanese forces in Manchuria and Korea (in addition to South Sakhalin and the Kuril Islands) in fulfillment of promises they had secretly made to the US and the UK at the Tehran and Yalta Conferences.

Right on Wikipedia.

the first bomb was dropped on 6 August, the Soviet Union declared war on the 8th. But contrary to American expectations and post-war claims, the author’s diligent research in the Japanese sources demonstrates conclusively that it was the Soviet declaration of war, not the atomic bombs, that forced the Japanese to surrender unconditionally.

Geoffrey Jukes review Racing the enemy: Stalin, Truman, and the surrender of Japan by Tsuyoshi Hasegawa