IMO, it has a lot to do with the drug culture. Ever since the beginning, illegal drugs have been linked to minorities.
not gonna weigh in on this whole conversation since it has started with this notion of a seemingly stable "american" culture contraposed against the various minority "subcultures" that, in actuality and original intent, make up that very "american culture." However, I will say that the linkage between minority populations and drug use has a lot more to do with a white-upperclass-male controlled media presence and economic disparity than "race" (ethnicity) or subcultural cohesion.
The first anti-drug movements (excepting the Temperance movement for alcohol) were against opium, cocaine and cannabis, all of which were vilified by a white, xenophobic population that associated the ingestion of these substances with the ethnic groups more dominantly engaged in their consumption as raw items. I distinguish "raw items" from processed because a large portion of the "patent medicines"--over the counter equivalents from the turn of the 19th century-- that were basically these same substances (cocaine, opium, cannabis), were being ingested by the white population in these more processed forms, usually tinctures, even as they bought into the anti-drug craze that was an essentially anti-'non-white' (put more simply, racist) movement.
Looking to cannabis alone, we can see from the congressional record that people were willing to testify as to the brazenness bred in "the negro mind" by the ingestion of cannabis: a willingness to look a white man in the eye, the audacity to step on his shadow. Cocaine, similarly, was associated with african inspired dance that was blending into the dance surrounding the popular music of the time: jazz. Such dancing was equally problematic for puritanical white aristocracy thereby accreting the negative appraisal by that group, who happen(ed) also to be the majority of those in control of both government and media (think: W.R. Hearst and yellow journalism).
Thus, the linkage between drugs and minority populations has always been bullshit. People, indeed all animals, have sought and ingested psychotropics. The linkage you proposed is one offered, top-down, by a group of elites, not one that arises from scientific study of real data--from the ground, up.