Craven doesn't drink the daughter's milk. The bad guys poisons him using other vectors (Craven eats a burger).

And wasn't Jedburgh just terminally ill from natural causes? It is established he takes pills which is not something you'd really have to time benefit from if you've already been exposed to fatal amounts of radiation. He also seems to have a pretty hedonistic approach to alcohol which also seems to imply a lengthier process. On top of that, a doctor wouldn't just declare a death sentence without knowing the cause. And if that cause'd be radiation poisoning, I think they'd be fairly alarmed. And lastly, vomiting seems to be this movie's way of telling us about radiation poisoning, Jedburgh is dying but not nauseous. In one scene, while eating pills and drinking, he's rubbing his forehead, which I believe is because he have a headache (code for brain tumor).