True, there's no categorical proof, but it's still far and away the most likely conclusion, in my judgement. It's true Garrett may have safe-houses, (it is implied he has one in Shalebridge in T2, we actually see one in OQ in T3), it's also clear that he has a more permanent apartment in SQ thoughout all 3 games (as he says in a T3 city section briefing "I guess this is home"). So I believe Home Turf refers to South Quarter, but it doesn't have to be his back yard.Oh, and by the same token, at no point in the game does he refer to Home Turf as South Quarter - there's no proof of it, one way or the other.
However, placing Shalebridge in Old Quarter doesn't move the Assassin map so it's not a problem. It was only an earlier map of Sola's that did this. If you look at the last one (page 30 of this thread) then you'll see what I mean.
Sola, is Lampfire Hills presented as a city section? (It sounds more of an outlying district or something).