But let’s assume that the Manhattan Transfer is trying to hide the use of Auto-Tune, in which case their recording engineer would presumably use a retune speed that approximates a “natural” value.
Retune speed is not a very relevant control when you aren't using auto-tune (proper name or generic) in fire-and-forget mode. If they're trying to cover up its use, they aren't using it in fire-and-forget mode. They're using it in graph mode, or they're using Melodyne, which has no retune speed adjustment.
But let’s assume that the Manhattan Transfer is trying to hide the use of Auto-Tune, in which case their recording engineer would presumably use a retune speed that approximates a “natural” value.