Maybe not override, but I'm sure he was given a say in the decision and his input was considered and given a lot of weight. And who knows, maybe Loomis wanted to cut Carr and Moore wanted to keep him. We really do not know.
At any rate, maybe Moore was in favor of keeping Carr. I could certainly see a young HC wanting to keep the best QB he has. Carr is mediocre, but right now he's by far the best QB on the team. Beyond that, keeping Carr was the only way they were going to have money to fill a few holes in free agency.
I was in favor of cutting Carr and rolling the dice with Rattler, but I could see how a new HC would want to be able to fill some holes on his roster and that meant keeping Carr.