Boy, that "ready.gov" page is garbage. Right before the section you quoted they state:
> Go to the basement or middle of the building. Stay away from the outer walls and roof. Try to maintain a distance of at least six feet between yourself and people who are not part of your household.
They should have used all that space about COVID-19 to better explain where to hide. I'm no expert, but I'm under the impression that if you're in a basement, it would be better to shelter against an outside wall, since all that dirt on the other side will effectively shield you from radiation coming from that direction (and you've got the rest of the mass of the building in the other direction).
Also...
> Stay inside for 24 hours unless local authorities provide other instructions.
Isn't that totally backwards? If you're dealing with fallout, don't you want to stay inside for at least 1-2 weeks unless explicitly told it's safe?