But they can both be right. You just need to think about it like someone without a political agenda.
Illegals working under the table have no federally documented income. Sure, their employer knows how much he pays them - but nothing is reported to the IRS. With no income, they can therefor apply for welfare.
They get paid twice.
There was a media expose on it, and the woman talked about how easy it was to further cheat the system by adding children that don't exist to her forms, which increases her monthly payout.