That's mostly wrong, particularly in the context of the proposal above. Fallout comes not only from the unfissioned nuclear material of the bomb, but also from the fisson byproducts and from neutron activation of other bomb components, such as the bomb case. And with a ground burst, or worse a bomb buried deep enough to create a very large crater (the above proposal), a huge amount of fallout is created through the neutron activation of the ground itself. This is true even with extremely efficient fission-fusion-fission bombs (e.g. thermonuclear bombs which use depleted uranium tampers), which produce a massive amount of neutron radiation and a great deal of fallout from the fission of the tamper which is caused by the fusion stage.