Nowhere on the site does it say that it is being run by Apple, but the fact that they are Apple certified means that the gang in Cupertino does have something to do with it. This is the second time that Apple has tried a program like this; last time it lasted all of three months and Apple failed to keep the store open. Apple and eBay are keeping a low-profile with the store, electing not to promote it.
If you're interested in checking out the Factory Outlet, click on the sourcelink. The prices being asked for the refurbished iPhone 5 models can save you $200 to $350 off the MSRP of a similar new factory unlocked, GSM flavored Apple iPhone 5.
Apple and eBay team up to sell refurbished factory unlocked GSM flavored Apple iPhone 5 models
source: FactoryOutlet via RedmondPie