Peril as you know you can't get much more rah-rah public school than us considering where DH teaches and we've had the public/state primary discussion many times as we are surrounded by some of the best prep schools in the country. However having talked to many of our neighbours with older kids I don't think that I would actually agree with your friend about it being more important to spend your money in the primary years - the consensus among most of our teacher friends with kids is that parental influence is much more important in the early years and can make up for basically any but a seriously awful primary experience.
However, as you get to secondary and especially the exam years the ability of a parent to influence a child's love of learning reduces and the school and especially the child's peers matter a lot more (ie. getting into a school where doing well academically is not seen as lame/swotty/nerdy).
This is not perfectly correlated with public vs state - I went to a private school where I was ostracised socially for doing maths and science as a girl (luckily transferred to a brilliant school for 6th form), while a friend of mine who did engineering at Cambridge went to a comprehensive which was incredibly encouraging of her doing science/maths/engineering. Also the previous school DH taught at was private and it was utter crap - I would never ever have sent my son there - demoralised teachers, aggressive bullying students and an atmosphere very unconducive to learning.
I certainly see here at our school that teachers help the boys massively with exams, are extremely proactive about appeals and remarks when exam results come in, and are right on top of university entrance requirements. That's what your money buys you at secondary level - not so much perfect A*s across the board, as that's up to the pupil as well, but fantastic advice about what universities are looking for and which will be most appropriate to the boy's talents and temperament.
The final thing to consider is facilities - most private schools invest heavily in sports/music/drama facilities and tend to do the "extras" to a much much higher standard than many state schools are able to afford, sadly. At the younger years it doesn't really matter if your kid has access to top-notch facilities at school as they are less likely to be specialising to a serious degree. However as kids get older and show a serious aptitude for something it's the private schools that have the facilities to develop that within the structure of the school without forcing you to take your kid out to clubs/training/camps that may interfere with academics. For example, at the boys' BBQ for the start of the half last night at the boarding house where DH is deputy housemaster, I was sitting with two boys who are going to GB trials for rowing, a boy who plays the clarinet to professional standards, and a boy who has just published a paper in an academic medical journal related to stuff he was working on over the summer with one of the science teachers here at the school. All this is possible together with staying in school because the school has the Olympic rowing lake together with a coach who represented GB at the Athens Olympics, the clarinet teacher that comes in plays in the London Symphony Orchestra, and the science teacher is a PhD from Imperial College London and helped the boy get a summer placement at his old lab.
So yeah, if you got to the end of that tome, good for you...we spend a lot of time talking about this stuff. FWIW we're going to start DS at the state primary across the street and just stay really engaged and on top of it, and move him if we feel it's not the right environment.