Adam had no incentive to kill OpenAI, but he had every incentive to get the org to reign in their commercialization efforts and to instead focus on research and safety initiatives, taking the heat off Poe while still providing it with the necessary API access to power the product.
I don't think it's crazy to speculate that Adam might have drummed up concern amongst the board over Sam's "dangerous" shipping velocity, sweeping up Ilya in the hysteria who now seems to regret taking part. Sam and Greg have both signaled positive sentiment towards Ilya, which points to them possibly believing he was misguided.