@Delirium. There are several problems with your hypothesis. First, there have been 4 unique mutations that account for sickle cell anemia. They have been estimated to have occurred roughly 6000 generations ago, or about 70,000–150,000 years ago (reviewed here; note I chose this reference because it is freely available on the web, rather than requiring a subscription). So, the mutations arose long before slash and burn agriculture existed.
Second, while it is true that heterozygotes are usually asymptomatic, under instances of severe stress, individuals with sickle cell trait (hets) can develop symptoms reminiscent of true sickle cell anemia.
Finally, and this is the most telling problem, the map you linked to shows the areas endemic for all forms of malaria. There are actually 4 species of malaria (Plasmodium falciparum, P. ovale, P. vivax, and P. malariae), with P. falciparum being by far the most dangerous. P. falciparum is primarily found in sub-Saharan Africa, and being heterozygous for hemoglobin S is protective only for P. falciparum. So, in fact, gooch is correct. Sickle cell anemia is much more prevalent in blacks, owing to their origin in Africa where P. falciparum is endemic.