Can you go into more detail? How much shielding? Sheilding with what? How heavy? How difficult is it to do? Etc.
The amount of shielding needed depends on what is being shielded. Lead blocks most things, and an ordinary lead apron used by lab x-ray technicians would block a lot.
Most radiation from non-weapon sources is alpha, beta, or gamma radiation, with gamma the most powerful and least common. Finding this kind of radiation would not be particularly alarming.
Neutrons are a different story. They are most often associated with fissile materials (meaning they can be split, and go BOOM!). Detecting neutrons is a very big deal.
The amount of neutron emission from enough fissionable material to start a chain reaction is remarkably small unless the material is brought close enough together to start a chain reaction. That happens only when the weapon is set off.
Neutrons can be absorbed by lead, but materials like cadmium are usually used instead (such as control rods in nuclear reactors).
The amount of shielding needed would depend on how "hot" the material being shielded was. (Generally, you need less than the public tends to think.)
My nuke experience is 20 years old, and I don't know how sensitive our detection capability is now. Hence, I have no way to estimate exactly how much shielding would block detection at any given range. I doubt the feds are giving that info out, and it would depend on what was being shielded anyway.
However, I certainly know the basics. I am extremely interested in finding out if neutron emissions were detected. I would also like to know what was meant by "fluctuating" levels of radiation, and what the suspicious noises from the hold were.
If anyone can confirm that neutron emissions were detected, that would be huge.