Interesting about St Paul's, Yellowtip.
Our brilliant local prep has much longer days than our state primary. The teaching is outstanding, class sizes are capped at 16. Our primary is also a very good school but having been in the classrooms of both schools on a fairly regular basis in the past I can see the incredible advantage the children at the prep get over our children at the primary.
The differences were staggering to me at first. Classes (at the Prep) had classrooms where the desks formed a horseshoe pattern, all children facing the teacher. There was nowhere to hide. Children were engaged at all times and you could have heard a pin drop. Time was set aside for collaboration and group tasks etc and children moved to another area for this sort of work. Children had a great deal of individual attention and time with the teacher. Weaknesses were ironed out early on.
Children in this (non selective) Prep I mention by and large go to the local Grammar school. A few go on to independent schools. Are these children at the Prep school not receiving 'tutoring' each and every single day? Are they not developing their intellect and working to capacity? By 11 they will have had 6 or 7 years worth of many hours of extra help and work that takes them way beyond the national curriculum & develops their curiosity and stretches them sideways.
Compare this to my son's school. It's a typical primary, they get good results and the children work well. Go into class and you'll hear a lot of noise. They'll be low level disruption and some monkeying around. Some children sit with their back to the teacher. She does the best she can and she's an excellent teacher. She has 30 in her class. Very few make it to the Grammar.
I read in the paper about the super selective Grammar near Sevenoaks, I believe. A mother was getting a hard time because she was tutoring her child for 2 HOURS each week for the 11 plus, that's 2 HOURS each week NOT each day. Surely this is but a drop in the ocean in terms of extra help? What can you really accomplish in 2 hours a week for a short period? Would St Paul's think a child like this was over-tutored? Would they think a child at the Prep just an ordinary child, who had received no help outside of school and therefore more deserving of a place?
Back to OP the headmaster's comment sounds very strange if meant seriously. As I see it if a child passes an exam to a school they deserve the place. Exams are not about regurgitating facts these days, you have to apply your knowledge and if you can do this accurately you deserve an academic place IMHO. Apparently scores at 11 can't be used to predict GCSE grades anyway. The system is, of course, skewed in favour of those at Prep schools such as the one I describe etc.