Having gone to public school (poor but bright in the old assisted place days) I can confirm that, though the advantage of much more games time and generally being better fed is a big factor.You'd be surprised, my state school played a few games against public schools and they were always the worst batterings we got. The public schools have always given burseries to freakishly huge kids to improve their teams and market themselves to the upper middle classes better
Worst I came across was playing an U16s match and on the opposition was a 6'5 man, clearly capable of growing a full beard, with thighs bigger than my waist. Theoretically I applaud having an African scholarship scheme that reaches places where people don't have birth certificates, but I remember being distinctly annoyed at having to tackle him.