According to a recent article in The Commercial Times, a Chinese business newspaper, PS3 consoles are being produced now.
In their story it's reported that Asustek Computer has been building PS3 machines since the first of the month and Sony is ready to receive a shipment of about 200,000 units by the end of the month. More manufacturers are to start delivering shipments in August as well.
It would be logical for Sony to want production to start as soon as possible to iron out any possible production problems early. As of yet there hasn't been any confirmation (or denial) regarding the story.