Agreed 100%. The station is under the parking garage, not T2. While it's closest to T2, the fact that the T2 ATS station doesn't connect to the parking garage like T3 does makes T3 the easier option.
Yes, but with my route (T2->ground floor->outdoors->Hilton->downstairs) you avoid going up and then down again, and you don't have to go towards the terminal (away from the blue line station) -- you only go down and towards the station.
Of course, you do have to stay on ATS for one more stop so that's probably some time penalty...