Actually, that's not true. We simply say that, as a matter of faith, it doesn't matter whether there was tweaking or not.
That being said, though science cannot rule out an occaisonal tweak, from a theological perspective I would find it rather uncharacteristic of the way God usually works. So a priori, I would tend to say there wasn't any tweaking, though of course no one can prove it.
Your first point is correct, thank you for pointing it out, and I also agree with your second point. Well said.