It is an accusation that has dogged the 34-year-old rollerskating academic from New Zealand ever since. Now the criticism of the dons has become sharper: Dr Woods is uprooting ancient teaching conventions by abolishing the student essay.
With scant regard for long-held tradition, Dr Woods is encouraging students to make presentations instead.
"Instead of just writing, I asked one group of mine who were studying Mill, Rousseau, de Toqueville and Marx to imagine that they were trying to persuade a group of aliens on Mars to adopt one of these political theories," said Dr Woods.
"I put them in teams of four and asked them to make a presentation. This got them thinking about method and about which matters most in the end, liberty or equality."
Dr Woods knows plenty about presentation herself. She hosts BBC2's "high policy" series, Compass, on Monday evenings, and is an interviewer for Radio 4's Analysis. But her colleagues - even those as media-friendly as she is - are fearful that this time she may have gone too far.
Vernon Bogdanor, Professor of Government at Oxford, believes the essay will always have a value in tutorials.
"An essay encourages verbal fluency," he said. "It is important for a student to put down their ideas in a concise way every week, although of course every tutor does have a right to their own methods."
At Lady Margaret Hall, fellow and tutor in politics Gillian Peele concedes that the university has probably been too rigid in the past, but she cannot imagine a suitable replacement for the student essay.
"It would be difficult to ensure that someone had understood and done the reading without an essay. They do force people to think and come up with an argument."
Dr Woods herself defends her modern regime of team games and corporate- style presentations at University College by claiming it is designed to reach students, rather than just indoctrinate them.
"In what kind of work anywhere in the world," she asked "would you walk into a room and read out your argument from several pages of A4?"
And her tutorials seem to be benefiting. At a college with a strong reputation for politics, Dr Woods's results are among the best, with a high percentage of firsts awarded to her students.
She arrived in Oxford from a lectureship in Auckland in 1987, and took a masters degree at Bailiol before becoming a research fellow at New College.
"I did immediately feel that in Britain enthusiasm is looked down upon," she said.
"It is always easy to appear clever here by adopting a lazy kind of scepticism. A lot of people do that because they don't want to appear stupid."
But at the same time Dr Woods can appreciate the freedom and individualism of a university system which has allowed her to innovate without asking anyone's permission.
"The very strength of Oxford, the wonderful thing about it, and about being in a small tutorial group, is that you can ask your students where their own starting points are.
"The first thing a teacher should be able to do is to enthuse. I have to make politics matter. Without that study is just bare and barren." For Dr Woods this means introducing teamwork and developing presentation skills. "An essay can be a useful way to zoom in on thoughts, but you need to get students to care. Another group of mine were studying Thatcherism, so I put them in teams of four and gave them each a quarter of Simon Jenkins' book to dissect."
She then invited the author up to Oxford to field criticisms.
"He said it was one of the most enlivening moments he had ever had inside a university. It also helped the students realise that the written word is up for grabs and that just because something is printed it doesn't mean you should not challenge it," she said.
And it seems that student feedback is encouraging too. Dr Woods has found the new obligatory questionnaires on staff performance returned by students very helpful.
Although not the ones which simply said, "Dr Woods is a babe."Reuse content