I'm sorry, but this is a lie. Online purchase of firearms means (1) that shipment must be from a Federal Firearms License holder to another FFL holder, and (2) that the receiving holder must do exactly the same paperwork, background check, etc, as his or her state requires of an in-person sale, before turning the gun over to the purchaser. This "anonymous online sales" meme is utter garbage.
Well unless you go to armslist.com and proceed with a private sale. But the seller always has the option to run the sale through an FFL if he/she wants to. Same goes for newspaper ads or ThriftyNickel ads when doing private party sales. Although some places won’t even carry firearms sales ads.