If looking only at jewelry-quality diamonds, there are millions of carats of diamonds mined per year, while there are generally thousands of carats of diamonds grown per year. In that regard, lab-grown white diamonds are much more rare than mined diamonds. It will take billions of dollars in capital to have a diamond growing facility with enough capacity to output more jewelry-quality diamonds than a single large diamond mine (though I suppose that is less than one WhatsApp, so is within the realm of possibility).

The Wired article about synthetic diamonds from 2003 was full of hype and misconceptions. Most all synthetic diamonds grown today are not flawless, and that is not by design. However, in the last couple years lab-grown white diamonds have become much more available in normal jewelry-quality ranges: http://d.neadiamonds.com/lab-created-diamonds/White-Diamonds

^ Disclosure: I'm an owner of D.NEA and have been selling jewelry-quality synthetic diamonds for many years.