According to the IRS, lottery winnings are income, and are taxes as such. Apparently, Michigan disagrees with this. Of course, the object of state lotteries is to be a voluntary tax on morons who do not understand the math behind probability. The bigger the prize, the fewer the winners, and the more morons buy tickets.
Telling the morons they can keep their food stamps even if they win will almost certainly pay for itself by more idiots participating. So perhaps, even though it looks unfair, it is a wise decision from a financial standpoint.