BUT..  Consider one of the parts of the plan that actually allows for a lowered cost to all citizens, is that the tax on food would provide a means for those who are not citizens to pay their fair share as well.

The Prebate returns the same amount to ALL taxpayers at the same amount to offset the cost of a seemingly increased tax.  They still have to eat, so the poor will be paying in, but simply be getting that part back (and marginally more if they are good shoppers)in the form of the check.  The FAIR part of it, is that those who may not need it ALSO get that check as well, as its distribution is not dependent on your income level.