I found this site a few years ago and I agree with the general thesis. However, it does not mean that a 'dirty' nuclear bomb cannot be built.
I imagine a thermite core surrounded by nano-milled plutonium. As we know, mushroom clouds are a feature of traditional explosions, so no need to fake this. The finely milled plutonium should spread outwards in a controlled pattern, and this will simulate the radiation.
Voila! One nuke.