The vice-chancellor of Oxford Brookes University this week welcomed a question from MPs about why her university missed its target for recruiting state-school students.
Janet Beer said she was "really pleased" to be asked because normally people were interested only in Oxbridge missing such benchmarks.
"I think access to higher education per se ought to be what we are talking about, rather than access to a few institutions," she told the Innovation, Universities, Science and Skills Select Committee.
Professor Beer said Oxford Brookes missed its benchmark by about 12 per cent despite strenuous efforts to recruit from state schools.
At the same evidence session, John Hood, vice-chancellor of the University of Oxford, criticised the benchmark for its lack of "sensitivity" and its failure to consider the degrees offered by Oxford.
"We have fewer than 300 applicants for 150 places in Classics, for example, but the spectrum of schools in this country does not prepare students for (such) degrees," he said.
An Oxford degree costs "substantially" more than the public funding awarded to the university per student and the tuition fee it can levy, Dr Hood said. "Some calculations ... indicate that the additional cost is as much as £8,000 a year."
He believed that his colleagues "would be minded to increase" undergraduate tuition fees, but only if there was a cast-iron guarantee that Oxford could offer needs-blind admission through loan schemes, bursaries and hardship funds.
Asked about the comparability of degrees awarded by Oxford Brookes and Oxford, Dr Hood would say only that they were "different".
The committee chairman, Phil Willis, later criticised both vice-chancellors for dodging this issue. He questioned whether their replies would "pass a GCSE essay".
• Figures released this week by the Office for National Statistics show that the Government is likely to miss its 50 per cent participation target next year. The provisional figure for the proportion of 17- to 30-year-olds in higher education in 2007-08 was 43.3 per cent, up from 42.1 per cent. The initial participation rate among 18-year-olds was 21 per cent.