I agree that they don't want a clergy calling the shots. They would prefer a constitutional theocracy, one with Christian principles written into the constitution, but otherwise democratic, with nominally secular leaders governing in accordance with biblical law. Americans tend to be fundamentalist Christians which means they prefer a "direct" relationship with God, and would reject any sort of ruling clergy. So an American theocracy would look quite different from an Iranian one, and would still be generally democratic.
(Why do I have to repeat these things?)
(Why do I have to repeat these things?)