Oh alright, I don't think I ever remember seeing/hearing that. But 9 times out of 10, I see Cov of Noah used as an artifact anyways, so it usually doesn't matter.
What if I played Weapon of the Holy during battle, which discards itself, and played Trust at the end of battle?
Weapon of the Holy - "Holder may discard this card to decrease a demon’s abilities by 5/5 until end of turn."