I think it's more that it is a replica. A very well done one. Just like the replica 190 in Sinsheim. You can't tell it is a replica, and has original parts in it, but it is not restoration of an actual 190 with a Werk Nummer.
Therefore it is not included in the registry of original aircraft.
An acft does not have to be in an official museum to be counted as original. There are dozens of original warbirds all over the US and Europe in private collections.
Here is a list of known original Bf 110's around the world, including the two restored complete ones in England and Germany.
Preserved Axis Aircraft