Most prep heads will point blank refuse to write references / support applications to schools if they know a DC would not have a chance in the selection process. They say it undermines the credibility of the prep and their professional judgement if they are 'sending' DC to schools that they are not cut out for. Not to mention, it is undue stress for the child. So I think senior schools do trust the professional judgment of heads that would recommend a group of kids year on year.
Thd head at the prep mine were at used to say that the only school she has no idea what on Earth they were thinking was the Harrodian and she would not attempt to call it. She said she could see no pattern as to who was offered a place and who was not.
I remember she said some schools put more emphasis on interviews than others - ie LU tend to rely on it quite heavily as they tend to take, shall we say, more confident / opinionated / 'character' types. Quite a few very academic but quiet / shy / 'bookish' DC did not get into LU, but they did get into LEH / SPGS and G&L and did brilliantly there and, in retrospect, these schools were probably a better fit (socially) anyway for those girls.
There used to be 'subject interviews' or 'general interviews' at KGS and lore had it that a general interview was basically an offer. Don't know if this is still the case?
SPGS was known for being slightly biased towards girls who were excellent at Maths, (rather than excellent at English) They also have Bute and Faulkner House which were essentially feeder schools, taking up maybe 20-30 places between them every year. Don't know if they still do? This was about 4 years ago.