A lot of people have talked about results - eg GCSE resuts, saying that their local state school is better than the nearby private school (why, of course).
Private schools are either selective or non-selective, and the selective schools almost always get 100% or close to it (for 5 A*-C). Those that don't get into a selective school go to a non-selective, so it is not surprising that their results are not 100% because they don't have the highest achieving children (rich people have thick kids too). They might only be 80%.
The league tables only measure the results for 15/16 year olds, but in independent schools, it is really common to sit the exams when children are ready for them, rather than according to their chronological age. This means that the number of exams sat in year 11 are often fewer than the child actually takes, so it is a smaller pool from which to get your 5 A*-C.
I've never heard of someone not being entered for an exam after a course of study just because they are not going to get an A or a B. If it does exist, then it could happen in either sector, and I would suspect more likely in the sector that cares more about league tables.
The two closest independent schools to me are always right at the bottom of the league tables (close to 0% A-C) and that with fees of £20k a year. Yet they are good enough schools, sending most of their pupils onto top universities - far more than the local (heavily-oversubscribed) comprehensive (35% A-C) could ever dream of.