I don't see how "on, at, or in the vicinity of" is anything other than crystal clear. BGC in general do not affect abilities cast from the outside in, as they don't say they do. Astral Hazing states, very clearly, that it does. If it was just meant to be a summary, than it would just say "in the vicinity of." What else could possibly have been RAI from "on, at, or in the vicinity of" instead of just "in the vicinity of?"
There is one (arguable) marginal benefit to being Astral Hazing as an Awakened character, which is that you are always in a rating 4 background count even if the area is worse than that, ie, if you would be in a Rating 12 background count, Astral Hazing gives you a "bubble" of 4 instead. It's kind of strange, though, and probably unintended, but some people over on Dumpshock really love this aspect of it so you may want to clear that one up with your player too.
If he is willing to take advice, though, outside of that one trick, Astral Hazing is really not good on an Awakened character. I'd consider using it as an Awakened if I wanted to sandbag like whoa, but it's seriously suboptimal.
If you want to make a character who is actually legitimately good at fighting other awakened:
Mystic Adept
Magician's Way
Sorcerous Parry
Arcane Arrester
Adversary [CS+Manipulation]
Mana Static
Mana Static is very good, and dramatically better than Astral Hazing for most purposes as you can (a) get way higher than 4 and (b) dump it on people at range without catching yourself. It also got very lightly buffed in an errata, so that it starts at BGC=hits and eventually rises to BGC=Force. It's very good for shafting Spirits (as they get disrupted at 0 Force, you can insta-kill spirits with no resistance from them), and for shafting other magicians and adepts.