Of course the question I have to ask is why we the taxpayers are footing the bill for an internal party function -- choosing who they want to run. There should be no public funding for that, and I go so far as to say the parties should either hold their own primaries with their own people and equipment, or be made to reimburse all of the states and counties in the country for any expenses related to primaries.
The "public money" is the pool of voluntary checkoffs on income tax. It's not from "general fund" or FICA or some other tax/fee source.