If that was their plan, they wouldn't have downgraded their claim from "Ukraine's going to set off a nuke and blame us" to "Ukraine is going to set off a dirty bomb and blame us". They greatly underestimated the amount of backbone North America and the rest of Europe possessed, and are desperately trying to find some propaganda claim that will weaken said backbone.
Except a modern nuke wouldn't be as destructive to civilians (comparatively) as a dirty bomb. Nukes, if detonated airburst, level cities but leave everything open for rebuilding due to the lack of huge amounts of fallout. Dirty bombs poison the soil with fallout for decades.
That's really not true at all. The "poison the earth for decades" notion refers to a cobalt bomb, which is a very "dirty" nuclear weapon fitted with a jacket of Cobalt 59 (ordinary cobalt metal) that is transmuted by the neutron flux into radioactive Cobalt 60 immediately before being vaporized by the extremely high energy of the atomic explosion. The energy of the blast turns the cobalt into a far finer particulate than any conventional explosion could, and Cobalt 60 (which is produced in very small numbers in an ordinary reactor - via transmuting iron into cobalt 59 and then the cobalt 59 into cobalt 60 - but far too little to readily collect) has very specific radioactive properties that make it a particularly nasty contaminant. The half-life of 5.27 years is long enough that you can't easily just wait it out, and short enough that the stuff is still extremely emissive. There's an inverse relationship between half-life and danger - the longer the half-life of a radioactive material, the less radiation it emits and thus the less danger it represents.
A so-called "dirty bomb" is just taking a bunch of radioactive material, wrapping it around some explosives, and detonating it. This scatters radioactive material around, but simple physics mean that the radioactive material is in much larger chunks and doesn't spread nearly as well. Simple radioactive materials don't generate the kind of hard neutron radiation you need to make more stuff radioactive, so it is just a lot of bits of radiation sitting around. And the thing about radiation is that it is pretty damn easy to detect. Cleanup from a dirty bomb would be expensive, but would simply amount to evacuating the area and sending a bunch of people in with radiations suits, firehoses (the vast majority of contamination would be outside, and can be washed down the sewers to be filtered out later), and Geiger counters (to track down and clean up anything that's left). Once that is done, the area can be reoccupied with no further risk. A fair number of people will have a somewhat elevated cancer risk, but it is not the doomsday weapon people think it is - it probably won't kill more than a handful of people other than those close enough to get caught in the actual blast.
Quite seriously,
each of the groundbursts from American nuclear tests in the 50s and early 60s probably contaminated Las Vegas more than a hundred dirty bombs could.