I recall watching a documentary where the reporters got diamond merchants to test some diamonds. Many of the synthetics were easily spotted but one - from a new technique or something - was only spotted because it was "too pure".
The testers that can identify a diamond's origin are quite expensive and usually only found at major gemological labs.
All synthetic white diamonds are "Type IIa" (no or trace amounts of nitrogen) while only 1-2% of mined diamonds are IIa. 97% of mined diamonds are "Type Ia" (clusters of nitrogen). It is possible that is what they were referring to about purity, but the amount of nitrogen is not a definitive indicator of origin.
This was a while ago though so I'd imagine the cat & mouse game has evolved for both sides.
It's sort of funny in a way... impure diamonds are worth more than pure diamonds... but then again, none of them would be worth much at all if DeBeers didn't control the release into the market (diamonds are not rare at all, and therefore only valuable due to artificial scarcity).