For a significant portion of American history there was an established difference in the distribution of the ability of people to own property. More recently there's an established difference in the distribution of the ability of minorities, students, and liberals to vote in certain states (NC, WI, TX, among others). There was an established difference in the incidence of AIDS during the 80's. There are established differences in the distribution of outcomes related to conviction of minor drug possession, soliciting prostitution, and a host of other non-violent crimes. Heck, there's an established difference in the distribution of police pulling people over or otherwise detaining people without cause in many municipalities.

Trying to justify discrimination by referring to the direct result of discriminatory behavior is obscene.