...actually, Quistis says in the game that she was "...adopted, but it didn't work out, so I was sent to Garden when I was 10."
and Irvine did go to Garden.... he just wasn't a SeeD. otherwise why was he hanging around the GG quad in disc 1?..... and why did Martine, the GG headmaster, assign him to a SeeD mission unless Irvine attended GG and was therefore required to obey Martine's orders? you can tell he's all talk, and wouldn't have gone on the assassination mission unless he really had to. (And I think he also knew that Edea was really Matron.)
also, Quistis' mannerisms and behaviour suggest that she was perhaps made to feel inadequate and insecure at an early age- after the SeeD exam she tells Squall what a crap teacher she is. I mean, she teaches Balamb's two star pupils- Squall and Seifer, and got her instructor's licence at the ridiculously young age of 17.... so she can't be that bad, can she? And how does an adoption 'not work out'? I sense some rather dark undertones there. *aargh, extrapolation*