https://www.gia.edu/sites/Satellite?c=Page&childpagename=GIA...
The IIDGR [1] company makes a series of devices (DiamondSure, DiamondView and DiamondPlus) that will indicate whether a diamond is a natural (and if so, of what type), or flag it for further characterization. One system will flag type IIa naturals for further analysis, as they resemble the best of CVD synthetic diamonds. Microscopy + (IR, fluorescence, and photoluminescence) spectroscopy distinguish a stone's origin to high confidence. Even though the best CVD stones have far lower impurities than the best naturals, they have internal strain patterns (optical birefringence) that can be diagnostic.
Most jewelers don't have these machines, but they are available as a service.
Faceted CVD stones have been seen up to 5 carats [2] and 10 carat stones made by HPHT are known [3]
[1] https://www.iidgr.com [2] https://www.gia.edu/gems-gemology/winter-2016-labnotes-CVD-s... [3] https://www.gia.edu/gems-gemology/winter-2016-labnotes-blue-...
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).