The president of Universities UK has vigorously defended the sector against allegations that universities are discriminating against privately educated applicants.
Geoff Lucas, general secretary of the Headmasters' and Headmistresses' Conference, accused the sector of "Eton-bashing" in Times Higher Education last week.
He denounced research showing that state-school students achieve better degrees than their private-school peers with the same A levels, saying it was flawed.
This week, Steve Smith, head of UUK and vice-chancellor of the University of Exeter, argues for more "differential" A-level offers - offers that are lower for students from state schools than those made to independent-school applicants.
He accuses Mr Lucas of failing to examine primary sources before rubbishing the research, and of "relying on assertions that have been refuted".
His comments are echoed by Bahram Bekhradnia, director of the Higher Education Policy Institute, in a letter to THE.
Mr Bekhradnia writes: "It won't do for interest groups and others with axes to grind to misuse or misrepresent research in this way. It is incumbent on all involved with education to distinguish between evidence, rhetoric and opinion."
Mr Lucas claimed that "schooling effects" were small and that other factors such as ethnicity had a greater effect.
In this week's THE, Professor Smith says the effects are small, but still significant.
Factors such as ethnicity may influence dropout rates but have "nothing to do with the existence of a schooling effect", he adds.
He cites research dating from 2007 that says that, given the differences in higher education achievement between state- and private-school students, contextual admissions were "not only justified, but did not go far enough".
The UUK president also cites a recent analysis by the Sutton Trust that found that when comparing like-for-like students, those educated at independent schools were 4 per cent less likely to achieve a first or 2:1 than their state-educated peers.
This week, preliminary figures released by the University of Oxford show that the percentage of offers made to UK state-school students had risen to 56.4 per cent for entry in 2010, up from 53.9 per cent in 2009.