Plot question - spoiler alert

Does anybody know how Mel's character contracted the Thalium (sp?) poisoning... there is a scene where the black op's guys are talking about that it would be consistent for him to have contracted the same poisoning as his daughter through contact, as in, let's set that up since it gives us plausible deniability... and later when on the phone, the CEO says "it's done", so is it definitely that they poison him, e.g., the cheeseburger you see him eating right after that phone call but before he "rear ends" the assassin car... OR, and this was my first impression, he drank some of the poison milk found in his daughters apartment on purpose because his death from the Thalium would lead investigators to find the tainted milk in his fridge... it could not be covered up again? That' want I thought because after they kidnap him, when he is already coughing from the poison, they take him to the steam tunnel to apparently expose him to the radioactive gas. Makes no sense if they were the ones that put the poison in his food. But if that was his plan, why would he then decide, after escaping and getting back home again, to go on a killing spree... just makes no sense.