(Can Japan really be that stupid?)
Yes! Remember they attacked Pearl Harbor knowing that they’d awaken a sleeping giant. Then they refused to surrender after the first atomic bomb wiped out Hiroshima. It took a second and almost a third to get them to surrender.
There were reports that the Emperor was planning to surrender after the first nuke, but there were rogue elements in the military who were planning a coup if that happened to prevent a surrender.
(The doctor survived because his hospital was on a hill and the radioactive fallout mostly stayed in the city at the bottom of the hill, and then they were fortunate enough to have a rain storm, which cleared the remaining fallout from the air.)