Sounds like some of this story may be B.S.!
1st - anything that's going to emit that much radiation that it would kill a person would most likely have tripped NEST rad monitors as it was moved into and around the country.
2nd - anything that's going to emit that much radiation that it would kill a person would/should have left a trail of bodies along it's path.
I'm not buying this story.
Also, a real nuclear weapon (not a radiological bomb) does not emit enough radiation to kill a person unless it has been damaged and then it would be, as you said, setting off alarms and leaving a trail of bodies.