That was the predictions at the time. Although I’ll concede it’s war and that may have been grossly exaggerated as a reason to drop the bombs. Maybe it was right, though.The US were bombing Japan with impunity before the A bomb - Japan had all but abandoned combating in the air with their few thousand aircraft being held back for 'kamikaze' missions in the event of a ground invasion ...
The Soviets had successfully repelled Hitler - a victorious army is a lot different to a demoralised one ... yes a ground invasion would have cost lives ... but I'm not sure where the 'millions' come from - especially when you consider the air support would have been overwhelming ...
The Japanese were loyal to the cause. They preferred death to the dishonour of surrendering. Considering the number of Japanese that would have been fighting to the bitter end, it may well have ended up in the millions and drawn the war out for at least another year or 2.
... not that I give a ****