You can buy a 'Rolex' very cheaply; get the right one, it'll work as a watch perfectly well. You could graft bits from a defunct real Rolex into it, or add a couple of bezels etc. Doesn't make it a Rolex.
Airworthiness for a flying aircraft (of any kind) is, as Rich says, paramount. But, again, the aircraft has to be registered as what it is - or started as - not what it might like to be when it grows up. Part of the problem Flug Werk had in the UK is that they were regarded by the CAA as a new design and the UK doesn't have an equivalent to 'Experimental' or 'Limited' categories. Representing it as a Focke Wulf wouldn't have helped.
The certification for flight process by most civil aviation authorities has
nothing to do with originality, as long as there's an identity and the parts and work go thought the right processes, as Rich has said. The FAA is smart to avoid getting involved in the question of originality as such, like most other equivalent organisations.
Interestingly though, precedent does count in the paperwork. There are notable exceptions where the (very non-)academic paperwork means there's a selection of one model high-top P-51s flying and 'none' of the other; and why CAC Mustangs are 'rare' in the US. In those cases the paperwork (though the people) is actively involved in distorting the provenance of the airframes.
Sure, we regularly get people talking about the "grandfather's axe" and how if it "walks like a duck" etcetera.
Fact actually is the market value depends on originality to some degree, and try selling (or even marketing) someone a Flug Werk FW 190 as a Focke Wulf and see what happens.
Likewise any heritage organisation that's really interested in history (such as national museums) is going to be real careful over choosing between the wannabe and 'the real thing'. And that's a global phenomenon, not restricted to any country. The only differences around the world are to do with local trading laws over mis-representing collectables. The collectors - whether of Monets, Ming or Messerschmitts are all after as much originality as they can afford, and check
hard to make sure it's as original as claimed.
Does anyone here really think Paul Allan's Flying Heritage would be just as happy with a Flug Werk 190, and a Stormbirds 262? All that money and effort spent to get the Flying Heritage airframes 'just so' that gets applauded here is because it adds value and retains originality of the design. Both historical and a notional cash value. If the originality was irrelevant, no one would be interested in going to see them.
If the difference wasn't important, I'd be selling you these rather nice Faberge eggs my jeweller friend's knocked up in his shop.

Regards,