Major gemological labs can certainly identify a diamond's origin (mined or grown). There are many characteristics that can identify origin, and color or clarity is rarely used as the conclusive indicator. Here is a semi-recent study of synthetic diamonds from my company: https://www.gia.edu/gems-gemology/spring-2014-ulrika-hpht-sy...

You are right though, gem-quality synthetic diamond technology didn't come around for several decades after this mine started producing.