Kochen-Specker rules out non-contextual hidden variable theories and Bell's theorem rules out local theories. I thought this was an interesting paper, particularly the authors' conclusions:

That non-locality is in some sense a consequence of contextuality has been the lore in the field for a long time, I think, with the usual argument being that the spatial separation employed in Bell tests is merely a way to guarantee the compatibility of observables, which is otherwise a problem in Kochen-Specker tests (basically, in real measurements, due to errors, you never have perfect compatibility; but for anything other than perfect compatibility, the notion of (non-)contextuality doesn't really make sense). Recall that Bell derived the Kochen-Specker theorem first, and then went on to prove the theorem that now bears his name, pretty much exactly because he thought that only the locality constraint can make sense of the assumption that the measurements shouldn't influence one another.

But what they're doing in the paper seems to be something different, some kind of set of Kochen-Specker measurements which 'combine' to a Bell test; I'll have to take a closer look to see how exactly that relates to the above, if it does.

In any case, I suppose the point of view that the main no-hidden-variables theorems, meaning Leggett-Garg in addition to Bell and Kochen-Specker, are really just different aspects of 'the same thing' is becoming more and more widespread; I think it was Arthur Fine who (late 70s? Early 80s?) first argued that this 'same thing' is the impossibility of finding a joint probability distribution whose marginals are capable of accounting for all experimentally observed correlations. From this point of view, the three theorems really just differ in how they attempt to ensure the independence of measurements---in the Bell case, it's locality, for Kochen-Specker, compatibility of measurements, and for Leggett-Garg, the 'noninvasiveness' of measurement.