Will AT&T unlocked a used iPhone 4S bought elsewhere?

So, I'm looking to pick up a used iPhone 4S for myself soon, since lots of people are selling theirs now that the 5 is out. What I want to do is get an AT&T unlocked phone to then use on the t-mobile network. But I've noticed that used factory unlocked phones cost $50 to $100 extra over a locked phone. So my question is, If I go buy a used 4S from craigslist, ebay, etc, that's no longer on contract but is still locked, would I be eligible for AT&T to factory unlocked the phone? Would they do that for me? Or will they refuse because I didn't buy it new from them?

Added (1). I know that there's other ways to unlocked an iPhone, but I really want it to be FACTORY unlocked, so it can still take any new updates and things like that

AT&T will usually only unlock the phone if you are the (ex-)contract holder with them. What you could do is to ask the prior owner to call AT&T for the unlock or to get the factory unlock yourself from one of the big online vendors like http://www.cellfservices.com/ as they don't have contractual requirements like AT&T itself.

It is possible to unlock iPhone 4S with the following factory unlocking service: http://www.fastgsm.com/en/apple/apple/iphone-4s/unlock/country-network
Only listed providers are supported but AT&T is one of them and it's really cheap. The unlock is permanent and granted by the carrier, the only risk is if the iPhone is blacklisted, so you should be sure about the origin of the phone.

It will be factory unlocked if you get from here
http://www.vunlock.com/