Don't see any contradiction. It doesn't matter if the Founders trust the "solids" or not. They are dead if they don't accept their terms. Founders lose, one way or another. The best they can achieve is elimination of a handful of solid races while their own race dies. Total loss from their point of view.
It matters very much whether they trust them. They wouldn't trust them to accept the cure, let alone to surrender in order to be given a cure. (Which may be fake, for all they know.) And they might
lose by getting ill and dying, but that doesn't mean that the Federation and its allies would
win, especially if angry Founders start an even more aggressive campaign, and if the Jem'Hadar continue what they've started.
Or, an even better scenario: the Founders pretend to surrender, are given a cure... and what's stopping them from launching another all-out attack?
Even under the assumption that the Alpha Quadrant forces are too weak to do that at that point - although I don't believe that the Dominion Alpha Quadrant forces would surrender completely before they got a cure that might be fake anyway - the Dominion is huge and includes many worlds and many more forces that can come out of the Gamma Quadrant.