There is a peculiar slippage in this argument, namely that the welfare state is good for poor people, and that therefore they are 'anti-poor' if they are anti-welfare state.
But the welfare state is not good for poor people. It keeps them poor. As Marx said of the poor law in England, poverty is so endemic their, they made it into an institution. Why should those Kentuckians be glad of living on food stamps. Living on food stamps sounds like a wretched existence to me.
That the Republican Party should capitalise on the resentment at big government is perverse, but not that poor people are hostile to the state.