Although i am a Cambridge applicant, from talking to tutors at open days it did come across that admissions tutors like to 'engineer' the combination of students they admit to produce an environment with a range of different backgrounds and personalities which will fit into and add to, their current student body. I personally think that politics may play a large role in whether you are pooled or admitted, because i think that is one trait that i think colleges would like most of their students to have in common. For example i can imagine a college such as kings in Cambridge (so left wing they have a hammer and sickle painted on the wall of their bar) would never admit someone who came into interview with strong right wing views; and at the same time im sure many colleges with more right wing views are happy to accept them if they have excellent application stats.
What im trying to say is that im sure the colleges came to an agreement as to where you would fit in best socially while studying at oxford, ( after all the admissions folk are sure to be excellent judges of character) rather than the one you initially applied to, and as you mentioned that St annes is quite left wing; you probably will fit in much more there than at Brasenose.
btw, i dont know anything about oxford college reputations, I can barely name 3 of them.