If my memory serves, I think he's right in saying that the VIRGINIA was the first vessel on which armoured construction was initiated.
You are correct in noting that the Eads ironclads were the first in battle, but I believe that their construction began well after construction on the VIRGINIA commenced. Again, if my memory serves, their construction was done very quickly (along the lines of the speed of construction of the MONITOR) and they were afloat and in battle before the VIRGINIA. Again, though, I believe that their actual construction occurred after VIRGINIA's.