i completely believe the report.
i went to Durham, from state school
everyone seemed to have 3,4,5,6 As at A level as mostly private school
i remember my first tutorials as being very daunting, i imagine many state-schoolers felt the same. we were used to classes of 20+ for our A levels, not 6 like most of my uni peers at private school
however, when it came to the first set of exams at the end of the first term "collections" as Durham calls them, the results were surprising. Many of those confident articulate students didn't actually do very well. I came in the top 10. Astonishing considering that i didn't have straight As.
After 3 years, 2 of the 3 students who got a 1st were from state schools
all those that got a 3rd, failed or dropped out were from private schools.
So, imo private schools get you the As you need. They also give you the inner belief and confidence that you can achieve anything. Some state schools also manage this, or parents manage to instil this in their children, but the school helps.