After listening to this podcast and reading the associated article, I think I finally understand the difference between political and free market competition. The issue clarified was rent seeking, both how it is defined and why it is harmful. Robert Tollison, an American economist who specializes in public choice theory (wikipedia):
Rent seeking is the expenditure of scarce resources to capture an artificially created transfer.
Basically, it is harmful to give things away for free. This is because people will compete to influence your choice (of who to give to), but since you refuse to accept money, they will spend on things which do not increase your ability to conjure up more of the supplied good, e.g. a more convincing proposal or a more extravagant charity event. The surplus from the exchange is thus partly dissipated away. This type of behavior is known as rent seeking.