I think the idea is that you mostly sample the decay products, which are either going to be descended from neutron-activated non-radioactive material from the surrounding area and can be filtered out in analysis, or are going to be more exotic decay products from the nuclear material, which will have isotopes in proportion to those in the original nuclear material. But yeah, IDK how feasible it would be to filter out the immense amount of fallout from the remnants of the bomb
Every atom ends up separated from every other atom. Why do you think you can get an accurate measure of the impurities after it's mixed with the stuff around? And after those impurities get altered by the neutron flux.
I do think you can get a reasonable estimate of the ratio of the plutonium isotopes that made up the bomb because the natural occurrence rate of plutonium is exceedingly low and we have a good understanding of what would happen to it in the detonation.
I think Clancy simply needed a smoking gun as to the origin.
There are some radioactive species that occur only as fission fragments -- no irradiation of naturally occurring isotopes will reasonably produce them -- and so from there you can get back to the original isotopic composition of the fissioning materials. There are enough tell-tale signs of each of the major isotopes that it is easier to separate them out than you might think. It is very, very possible, for example, to use a neutrino detector to tell exactly what is going on inside a nuclear reactor's core, which is not something you might realize is possible until you've seen it done! (But neutrino detectors are very large, must be placed very close in, and are very, ah, obvious things to have around.)
This analysis is quite difficult, and I don't know that it has ever been done on an actual detonation (at least, no one admits to doing it; not that there have been terribly many opportunities to practice this), but there is no reason it can't be done.
(You're probably right that Clancy took some authorial license, though.)
For an example of what is possible, see the ruthenium mess in Europe from a few years back: https://cen.acs.org/safety/industrial-safety/caused-plume-ra... or https://www.nature.com/articles/s41467-020-16316-3 among others.