Actually, I have no idea how the Dominion's trustworthiness came into it.
See post #80. Knight Templar
alleged that Sisko had lied to the Prophets to win their support because there was no evidence that the Dominion had any intention of harming Bajor. So KT was assuming the Dominion could be trusted to keep its word.
A DEM is a way of solving a problem which comes out of nowhere, using previously unknown characters and a large dose of luck.
Not necessarily characters. It can be an event, an object, a sudden heart attack -- anything that comes out of the blue to solve the problem rather than being a logical outgrowth of the story and characters established so far.