I know about factory phones, but the OP was likely going the US-based phone route. Some European phones are also factory unlocked.
How does it feel to write "Wrong. Wrong. Wrong. Wrong Wrong. Wrong." on a forum? Does it feel wonderful?
Yes. I believe that there is also no such thing as a "factory unlocked phone". An iPhone becomes locked or unlocked when you activate it. It all depends on how the IMEI number is flagged in their activation server database. Some iPhone boxes are scanned into the system before leaving the factory as "locked" to a specific carrier while those headed to the HK, Singapore, Belgium, Australia or Italy are not.
I have no absolute proof on this but it seems logical to me that they would have one production run for the entire world and lock phones to a carrier in their activation database when they ship them out the door. Otherwise, they would have to set up separate production runs for each carrier. This guess on my part is also consistent with how the official unlock process works.
In countries that have carriers offering the service, the customer provides a fee to the carrier who in turn forwards the IMEI number of the iPhone to Apple using a special piece of software that only the store manager has access to. All the customer has to do is go home to sync their iPhone with iTunes and they will get a screen stating that their iPhone is unlocked just like "factory unlocked" phones have when you active for the first time or update the iPhone OS to a new release.
I think all phones are by default set to "unlocked" and the locking happens when the shipment goes out.