Peter Hamby has a nice debunking of some myths of South Carolina politics. For one, some instances of negative campaigning were widely discussed but never quite confirmed. For another, the negative campaigning that does occur may not work. See also my discussion of the academic literature on negative campaigning, which finds exactly that.
Jordan Ragusa adds another valuable point. Rather than assuming that South Carolina's "culture" breeds nasty politics in presidential primaries, consider this:
Because the primary system is an iterated process (rather than a one-shot, 50 state election), political "momentum" is critically important…Simply put, candidates who win early primaries like Iowa and New Hampshire are likely to receive greater support in subsequent states because of sophisticated or "front runner" voting (see this paper) as well as generate greater campaign donations and support. This, in turn, improves their chances for winning subsequent primaries. Because South Carolina is third in this sequence, there is an incentive for candidates to go negative independent of the state's demographics.
