Why the claim "Racism exists in Detroit" is absurd

i have heard that the way most people scam the welfare system goes something like this:

a man and a woman live together and have a child or two (or more). the man is employed, the woman is not. she goes and applies for aid, claiming to be without work and living alone with her child. he in turn claims to live at his momma's house for tax purposes. she receives every bit of aid (foodstamps, cash, housing assitance, etc.) that she can, which frees most of the man's income to be spent on new clothes or a new sound system for his caprice classic.

can you really object to this set up cow cud? it is the ideal american family! the man (fulfilling his traditional role as father) is working, and the woman (fulfilling her traditional role as mother) stays at home to take care of the house and children. the only difference is that these people are smart enough to remain unmarried to make more money.....