The "crude terrorist nuke" assumes that terrorists aren't going to be able to get that precision and technique and will only get a very small yield because the bomb will blow itself apart before the chain reaction can consume all the material. After all nation states took many, many tries to get it right
Of course fallout, especially from explosions on the ground to destroy hardened bunkers, silos, and sub pens can generate terrifying levels of fallout. It's just the prompt radiation from the explosion itself that usually isn't a concern.
https://en.m.wikipedia.org/wiki/Gun-type_fission_weapon
Can an organization get that amount of material as far as we know?
Even with all the work they put into making the implosion hold the fissionable material together it still apparently only consumed about 20% of the material.
But yeah its unlikely a terrorist org could get enough material for a "gun type" and the implosion type would also be very, very hard to get right
OTOH a plutonium implosion type device is a lot more difficult to get right, and is practically out of reach for non-state actors. On top of the device engineering difficulty itself, producing the raw materials is difficult too. The actual production of weapons grade plutonium isn't terribly difficult (e.g. a natural uranium fueled graphite moderated reactor), separating the Pu from the spent fuel with the PUREX process is fairly expensive and complicated.
we made a bit of a big deal when it was revealed uranium yellow cake was being produced in quantity
>In the Little Boy design, the U-235 "bullet" had a mass of around 86 pounds (39 kg), and it was 7 inches (17.8 cm) long, with a diameter of 6.25 inches (15.9 cm). The hollow cylindrical shape made it subcritical. It was powered by a cordite charge. The uranium target spike was about 57.3 pounds (26 kg).<