You're right, it seems to be just all over the place. My SA seems pretty forthright and she said there's no rhyme or reason to the offer (but she did say the SM has final say)--all consistent with what I read on this forum.
Yes that’s right - I believe generally your SA proposes for you to get the bag but the SM will have to approve it (wouldn’t surprise me if it may be different / have exceptions somewhere though). Depending on the SA style, some will let you know when they are doing the proposal while some won’t tell you until they got the OK from the SM and can guarantee that you will be able to get the bag.
Also, I think sometimes at least partially it’s your luck and timing!
(I edited my original comment to specify it was after the second visit with my current SA who was actually not the first I met. But I didn’t feel connected with the SA I got before and decided try again later)