From a Retired Nuclear Operator
Even in 1951 when this was filmed there were several sites still currently semi-operational.
The one where I was assigned for 25 years had facilities with walls made of concrete several feet thick and designed to withstand severe blasts. Whole floors of facilities were underground. For example you might think a building you are viewing was only two stories tall when actually they were five stories, with three underground. Parts of these buildings were designed for use as evacuation shelters stocked with supplies to keep many of its workers alive for a long time.
My point is there would probably be many survivors in these facilities that outside world may not be aware of. Even some buildings staffed with mostly office workers there were these "bomb shelters" for their survival.
Some of these facilities were not designed for nuclear processing and construction was not as great as those mentioned previously. There would be many casualties in these facilities, but I think there would be a large number of survivors in these locations.