The way the war actually did end suggests that it was really S31 who won the war with their attempted genocide, which weakened the female Founder enough that she would surrender. But Starfleet having no idea what S31 was up to, they had to go on what they knew, and without S31's actions, the Federation would have lost, if the Rommies hadn't joined their side. Ironically, that means that Sisko and Garak's war crime in ITPM was made unnecessary by S31's war crime. 
