If you already know all the different issues that were on her mind, good!
I still don't see how this means the popularity polls are compromised or flawed.
Your friend made a calculated decision based on what she thinks her odds are in each phase. Besides her "lucky break" of being a teacher in a top school which gives her child the same priority (which I disapprove of, why should teachers get the priority to enroll their children in the school they teach, is this NOT blatant cronyism, we can see how wrong it is when we look at other public service jobs. The equivalent is if we let every general and colonel enroll their sons under their command when they do NS. Just think about it. That's how outlandish it is), your friend is not really any more special than the thousands of other parents who have gone through the exercise. All parents weigh their chances at each phase. Parents who live within 1km of a super popular school like St Nicks, Catholic High or Rosyth are forced to weigh if they should apply for 2A in the alumni category of their alma mater which is not as good as St Nicks or Rosyth. But higher chance they will get in and if offered, they would be forced to accept it, if not try 2C 1km also have to ballot for St Nicks or Catholic High. Not really special lah your friend.
There are countless parents who still try to get into popular schools if they live within 1km of St Nicks despite knowing they have to ballot. There are also countless others who move to the vicinity for the purpose. You are splitting hairs over essentially nothing probably due to your own inability to understand stats.
The science isn't 100% exact because no science is, but it is still a science that is there and generally works to provide a mathematical picture.
I will speak to my MP about the unconscionable policy of giving teachers priority to enroll their children in a school that they work in.