Moreover they generally make the argument, have marginal tax rates explained and then rapidly go off looking for some specific welfare policy where this is sort of true.

Because if they knew about the welfare policy before they started typing, they would've actually mentioned it then - it's a specific problem, with several obvious solutions (i.e. don't means test at all or taper off more gently) unrelated to the concept of tax brackets (and potentially not related to the actual bracket index values themselves.