Not quite. At least the one I found is some trickle down economics myth.

The one op is referencing is more like the dollar is used to pay off the waitstaff, who pay their rent to the landlord, who pay their over due taxes, so that the government can issue a refund to the cafe owner. The dollar ends up back in the hands of the cafe owner, who puts it back down on the table with all the debts paid off.