These sorts of assumptions are the default in the climate change literature.  Few agricultural impacts studies account for crop migration or for the prospect that we might introduce new cultivars. I imagine the authors are following the lead of the climate literature there, though it obviously massively overstates the impact of cooling or warming  

I also think this highlights a wider problem with the nuclear winter literature. The scholars in the field are very obviously biased. Robock and his collaborators write almost all of the papers but clearly have an agenda. Just take a look at Alan Robock's website - flashing nuclear bomb gifs and pictures with Fidel Castro. 

• I followed Robock's work in solar geoengineering and it was also clearly biased. He claimed that solar geoengineering would knock out the monsoons, but his paper actually showed that solar geo would reduce disruption to the monsoon. Researchers in the field expressed frustration about Robock's meme, which he spread because he doesn't like solar geo. 
• If you look at the nuclear winter literature in the 1980s, all of the scientists say "this is bullshit". The only thing that changed with the second round of nuclear winter papers starting with Robock was that he used modern climate models. But the criticism was never about the climate model, it was about how much particulate matter would get into the atmosphere and how long it would stay there. So, the idea that modern science validated nuclear winter is just wrong. 
• A very prominent climate physicist told me that the assumptions in the Robock papers are turned up to maximise damage rather than to actually be plausible, and that people are scared to point this out because of the politicised nature of the debate on nuclear war
• The smoke estimates in the Robock papers didn't change despite a massive decline in the nuclear arsenal. 

Some thoughts:

• In your subsequent post, "Actually, All Nuclear Famine Papers are Bunk", you talk about the impressive, year-plus grain stores that farmers rack up each fall.  How much does this vary throughout the year?  Presumably a nuclear war that struck at the worst possible time (perhaps that May 1 that the Nature paper strategically chose?) would leave us with much reduced food stores.
• The Nature paper seems to imply that protein would be the toughest thing to scrounge up in a nuclear winter scenario, rather than raw calories.  This is probably less storable than other macronutrients like carbohydrates and fat?

I totally agree that it's ridiculous to think that people would just plant the same foods over again despite the obviously colder weather.  On the other hand, in a post-nuclear-exchange scenario, I would be worried that farmers might not be able to access the normal distribution networks for purchasing new seeds, or that it would be more difficult to repair / replace crucial planting equipment, or that farmers (especially in the third world) wouldn't have the information/education/experience needed to switch crop varieties successfully.  I'd love to read a paper or blog post where someone tried to game out how the negative effects of the war (on equipment, trade networks, etc) and positive effects (of adaptation to colder temperatures by planting different crops) would change the Nature paper's conclusion, either for worse or better.

I am not surprised anymore by the low quality of some papers published in top-tier journals