If US and Russia unload, say, 75% of their arsenals I'm pretty sure that is inaccurate. Not to mention there seems to be no consideration of the radiation levels in various foods?
Even back when the warhead and delivery inventories were much larger (100 times or so if my memory serves), a LLNL 3D simulation of "nuclear winter" resulted in a single nuclear fall (TAPPS, which I read when it came out and studied, was fraudulent, especially in it's use of a 1 dimensional model of the atmosphere (i.e. no winds, no oceans, etc.)). Not good, just like all too many volcanic eruptions in recorded or thereabouts history, but not the end of the world.
An overall radiation increase would small to immeasurable, the effect immeasurable. It would suck to be close and downwind of a warhead explosion unless you're prepared, further away not so good, but even in Cold War targeted US 10s of millions would have survived without lifting a finger WRT to radiation.