No, they don't "know" the Cardassians would never allow an atrocity like that. Why would they? They never cared about the Cardassians. They were a foothold in the Alpha Quadrant, and no more than that. They didn't treat the Cardassians as equals even when relations between the Cardassians and the Dominion were at their best.
How would they not know? They may not have cared about the Cardassians, but surely they had enough interactions to know what they would and wouldn't endure. They would've had enough evidence through Demars increasing intolerance of the dominion, and the pockets of resistance that started to emerge. They are obviously a proud race that would not sit idly by while millions of their citizens are slaughtered. That's obvious to anyone, why shouldn't it be obvious to the dominion? It's pretty ridiculous that they wouldn't know anything about a close military ally of a number of years..