If the only discrepancy is the fluff, I would be fine with it. If the character cannot ever use firearms and has four points of notoriety from it, then I would allow it. If someone wanted to play a mage who abhorred binding, considering it the equivalent of enslaving a sentient being, and would never learn or use the skill, then I would let them take incompetent: binding. Honestly - this is a set of incompetencies that will really limit the character, in her area (combat); I would much rather see something like this than the ever-popular (at least as an example

) incompetence: aeronautics pilot.
I would be fine with "Used to be awesome with guns", too. The character stats at creation are a
snapshot in time. If someone's background is that they were a mage, burned out from drugs and cyberware, and are trying to make it as a bitter street samurai now, I would expect them to have a relevant magical knowledge skill or two, but I wouldn't make them buy the mage quality and all of the awakened skills and spells that they had before becoming a mundane.
The only problem I have with the background is that it needs to make it more clear what an absolute limitation this is. It can't just be "Guns weren't challenging enough any longer". It has to be an unbreakable mental block, or an equally unbreakable vow to herself. With the incompetence quality, this character literally would
not be able to pick up a gun lying on the ground to shoot someone about to kill one of her loved ones. So while I would allow a "roleplaying" reason for the flaw, it needs to be a slightly more compelling one.