Reason I say this is .004" is nothing. Nothing unusual for FL dies to not size it down as small as Factory. Small base dies will take it down to factory sizes. I am surprised it wasn't more than .004".

You ought to measure the diameter of the chamber. You do that by measuring a fireformed piece, and then compare it to factory.

If the brass was fired in your rifle, and then FL sized, and you can't get back in the gun, that makes no sense. Think about it. You take a piece of factory brass that is a certain diameter, fits fine in a rifle. You fire it, the diameter grows some, has too, or you couldn't chamber it in the first place. You size it with a FL die, the FL die cannot expand the diameter greater than fireformed. Many of us on here only neck size. We don't size the case at all.