The ATT, T-Mobile and Verizon phones are all the same model. Once unlocked, they will work on any carrier except Sprint. They also have the same bands (due to the same model). The Verizon phone comes unlocked regardless if bought full price or not.
My ATT phone was unlocked via a web service ($100
)
Case in point, my phone is an ATT phone and it is on my Verizon account - the "registered IMEI" only means it is listed as "NON-VZW DEVICE" on their website, they still accept it on the network. This is due to LTE and is not the same for CDMA ONLY devices.