You only bought outright the phone if you paid the full price. Which is depending on the model between $449 and $949.
However if you did paid a subsidized price, between $0 and $499 or paid in Monthly installments you only "Own" the phone if it was paid off, either by paying all the installments or the term was up on your contract for the subsidized price.
Now here is why Apple wasn't showing the phone as blocked. Apple is listing a feature called "Activation Lock" were if a phone is lost or stolen and has Find my iPhone turned on the phone will not work even if erased / wiped without their Apple ID, because this is your phone and you either know your password or don't have Find my iPhone turned on (if on iOS 7).
What the carrier can do and has done is blocked the IMEI which is like a serial number for the cellphone carrier. This prevents the phone from being used and was the method of blocking cellphones from being used before activation lock existed when stolen. Carriers do this to prevent theft because thieves won't steel something they can't sell (an unusable mobile phone)
To fix this call ATT and see why the phone was blocked. Did they block it because it wasn't paid for in full? Maybe you can concise them you will pay the difference.
Or did the account holder ask for this phone to be blocked and you are all good on payment? If this is the case I would show them the fact you paid for this device and are the true owner.
