It depends on whether your view is of the thing. If it's a museum piece, then no it is not the same thing. I'd feel this way about a very early one (I had S/no about 1500, from 1973) and I think that if you are keeping it as a historical artefact then it's a valid view. If however you want to use it as a high performance item, then modifications are allowed and yes, it remains an LP12, albeit a modded one.
This debate runs continuously around classic cars and bikes. If you had Steve McQueen's motorbike from The Great Escape, would you feel comfortable about fitting a different engine? Likewise the IoM TT winner from 1965. No way, it wuld be a travesty. If however you gave me a 1980 Caterham 7 with a blown engine, I'd be more than happy to drop a fuel injected Zetec in there, complete with 160-odd bhp, or a Fireblade engine, and throw away/sell the knackered old X-flow. It's all reversible, after all.