I really think this Background sticks out like a sore thumb and doesn't actually play by the rules it exists in.
The basic idea of character creation seems to be, the combination of Background and Role is supposed to be the starting point for determining the PC's place in a world. For example, a Ministrorum Warrior might be a Battle Sister novitiate, a Frateris Militia member, or a Redemptionist (or whatever else seems fitting). Meanwhile an AdMech Warrior may be a Secutor, a Skitarii, a mercenary with a thing for augmentations that makes him work for AdMech more often than not, whatever. The point is, every combination is supposed to be justifiable in some way, and the background bonus is supposed to be of some use for a wide variety of characters (not necessarily always equally useful, just applicable).
Enter AAT, a Background that keeps saying: you're a psyker. Except you aren't, not by virtue of getting that Background anyway. The bonus? You're Sanctioned. If you take the Mystic role, you're a Sanctioned Imperial Psyker. If you take any other role and the Psyker Elite Advancement, you're also a Sanctioned Imperial Psyker, though with different inclinations.
But what about those people who don't take the Mystic Role or the Elite Advancement? I guess they're psykers as well, because somebody took the effort of taking them to Holy Terra and Sanctioning them. They even get Psyniscience at Rank 2 (as in, a trained Skill) to show for it, despite the Skill being only available to people with Psy Rating.
That's extremely constraining, and I don't think very accurate fluff-wise - or are only psykers ever counted among the ranks of AAT? The tough voidsman serving on a Black Ship? Sanctioned apparently. The clever scribe keeping tally of the transported wyrds? Also Sanctioned. The Emperor-damned Untouchable bounty hunter specializing in finding Wyrds and bringing them to the Black Ships? Apparently, also Sanctioned, and somehow able to see the Warp despite being a soulless abomination. Heck, the guy who fixes the Astropath's toilet is apparently also Sanctioned. Do these guys just open up all entry points on those Black Ships while hovering above the Imperial Palace and throw everyone out for sanctioning?
The other side of the coin is, due to AAT having a monopoly on their indiscriminately conducted Sanctioning, it's also extremely limiting for those who want to actually play Sanctioned Psykers, because they have to take AAT as a Background. Want to play a rugged combat psyker who spent the last ten years on the various fronts, fighting alongside the Imperial Guard and not having much contact with AAT structures in this time? Nope, you can't give him the IG background, because then he'd be a witch, an unsanctioned wyrd existing at the whim of the Inquisitor and the mercy of the fellow Acolytes should they find out.
Best you can do is take the AAT Background, the Mystic Role and spend almost all your starting exp on Specialist (IG). But what if you wanted your Psyker to be more martially inclined than the Mystic role suggests? You don't have enough exp for that. At best, you're an AAT guy who's Sanctioned without a Psy Rating (see above) with a Warrior Role and Specialist (IG) - and then you have neither Psy Rating nor combat-y Talents to show for your story of being a battlefield Imperial Psyker issued to the IG.
I think what the AAT background needs is divorcing the notion that all it's members are psykers, getting rid of both Sanctioned and Psyniscience, and creating a new bonus that'll be more useful for a wider number of character concepts. Sanctioned should instead be tied to either a Role (perhaps splitting the Mystic into Sanctioned Psyker and Wyrd would make sense - both would get Psyker, SP would get Sanctioned as well while the Wyrd would get an extra bonus to compensate) or available as an Elite Advancement (presumably, character creation only).