And it was struck after the layer separated from the rest of the coin. Not sure what you mean by "dual struck".
Surely either the obverse or reverse design would be a lot less clear if that had happened, right? I figured the unique presence of both obverse and reverse features on both sides arose because this is a really thin fragment, struck as a fragment, with both dies contacting its metal.
I think it's more of a progressive indirect die transfer due to it being so thin and not that it was struck twice. If it was double struck they would put that on the label also.