Until very recently Cambridge had an explicit target for state schools, completely separate to the contextual offers. And yes, they were giving offers to equally-privileged state school candidates who were less strong than private school students they rejected.
And that was reflected in university results. Cambridge detailed that in their own analysis.
Now whether that discrimination by education sector is something we want as a society is another matter. At a society level, you could argue that it's worth doing.
The aim is greater equity (whether it acieves that or not is a different matter). And Oxbridge does typically benefit an equal-ability student with a lower SES more than their higher SES academic-equal, since the higher SES candidate typically has other options, so there's a society-wide benefit there.
But it isn't meritocratic. And being non-meriticratic for more than a small percentage of students does damage our elite universities.
Cambridge have now changed their criteria. Probably as a result of that analysis. Whether the new criteria will work better remains to be seen.
Regardless, people will always find the best way forward for themselves. In many private schools (including DDs) in the last few years, that has included changing to state for 6th form for many students who aspire to Oxbridge. You may not like it @tortoise18 , but that's absolutely the case.
DD is still quite young, but it's something we'll look into the current stats for when we get closer, if that's a route she's interested in.