Then, last Monday, on Start the Week, Melvyn Bragg treated the professor with shocking contempt and discourtesy, even by his own fairly low standards.
Though clearly affected,( she really hasn't managed a smile thus far) Williams rises supremely above all the sewage that is gathering around her. It would, she gently says, be unseemly to criticise another BBC broadcaster and the tabloids; this is what happens whenever black intellectuals try to communicate their concerns in measured, reasonable terms. "Black women in particular are turned into caricatures and monsters. It even happened to Toni Morrison after she won the Nobel prize. Of course it is isolating and hurtful - I couldn't have anticipated this, and I do not recognise myself in the things that people are discussing in my name."
But then, maybe these unpleasant events are an illustration of the central theme of her talks: the extraordinary reluctance of influential white people, even liberals, to accept that race is a serious problem and that they are now part of the problem instead of being - as many once were - allies in finding solutions.
As Williams puts it: "Liberals, I believe, have a lot of difficulty with discussing this because they have invested so much in the image of what good people they are. At the same time the discourse of race is overlaid by such a tremendous range of associations that it is impossible to consider the subject with rational and informed voices, with grace and mutual respect. What is heard is often not what has in fact been said. But perhaps most worrying is the growing perceptual distance between most blacks and most whites."
These observations would be recognised by many minorities on both sides of the Atlantic.
Williams argues persuasively that certain myths remain unshakeable, despite the evidence: "The United States deems itself classless with almost the same degree of self-congratulation that Britain prides itself on being largely free of racial animus." Real evidence is not allowed to intervene.
She is right: with income differentials as bad as in some Third World countries, the American dream is still said to be available to all. In Britain, we absurdly cling to the belief that compared with Germany, France or the US, ours is a veritable garden of multicultural bliss. Bragg, for example, stated complacently that our nationality laws are far fairer than those in Germany, where Turkish children are not entitled to German citizenship. But what of the fact that every year, this country deports scores of British children because of our nationality laws?
Perhaps there are benign reasons, too, for such reactions. Most enlightened white people want society rid of racism. Their impatience and utopianism are impairing their perceptions. Williams calls it the "I think, therefore it is" school of idealism: "I don't think about colour, therefore your problems don't exist."
This may help to explain the backlash against "political correctness" a label that is used instantly to discredit any attempt to redress inequalities. Significantly, the assault on it in this country was launched not by the rabid right but by egalitarians such as Simon Hoggart and Melanie Phillips.
Manifestations of racism have become more subtle. Once, the main problem was that murderous redneck down south. Now it is just as likely to be highly paid directors of Texaco or, in this country, solicitors' chambers which can say all the right things.
And, says Williams, there are all those daily slights: people not letting even someone like her try both shoes in a shop, or the silent panic when she moves into a nearly white, "respectable" neighbourhood.
These are not just the views of a paranoid professor. Reputable people such as the American lawyer Maurice Franks also believe that: "In every area, America institutionalises the quibbling over marginally relevant minutiae, as diversions perhaps from the unpleasant task of confronting and dealing with the real problems ... The United States is a racially divided house."
But might it also be, I suggest, a dance of denial on both sides? If white people disavow racism, are blacks also guilty of disclaiming the progress which has indisputably been made?
Williams accepts that she may have underemphasised achievements: "I am an example of exactly that," she admits. "A beneficiary of all the gains of affirmative action." This is refreshing at a time when so many are rejecting the laws which they feel institutionalise anti-white discrimination and also demean blacks. She is less candid on why so many blacks have joined this reaction and have gone further, claiming that racism is now not a problem but an excuse. The conservative writer Dinesh Desouza, who argues this in The End of Racism, is himself Asian. The black film maker Charles Burnett recently described middle-class African Americans who "have taken on white attitudes towards other blacks, calling them shiftless and lazy".
Patricia Williams argues - implausibly - that even conservative blacks such as Clarence Thomas do not reject the reality of racism. But the truth is that he did, until he needed to use it as a cynical defence tool during his hearings.
We then go on to discuss the difficult subject of black responsibility, and why some ethnic groups are doing better than others. This issue is now being raised here by people such as Professor Ceri Peach, at Oxford, whose research leads him to conclude that Asians are more "Jewish" and Afro-Caribbeans are akin to the Irish. The answers are complex, and cannot simply be attributed to stereotypical assumptions, or the old tricks of divide and rule. And surely there are ways of by-passing racism through some kind of self-reliance?
"Yes, and I practise it, as do many black professionals," says Williams. "We have networks, provide scholarships, take care of our own. But there is only so much self-help possible if, say, there are 60 children in a poorly-resourced classroom."
But why are Caribbean blacks making more strides than African Americans? "Because," she says, "they are seen as immigrants with nice English accents. Research indicates that second-generation children are experiencing the same problems." That thorny subject we leave unresolved.
History is her other preoccupation. Is this not just demanding unending white culpability? Is it just possible that having too heightened a sense of slavery or the Holocaust may in fact be as damaging as forgetting completely? No, she asserts. She is not interested in guilt, just in a sense of history which may warn us, provide lessons, introduce caution.
But it is a fact that white people have been banished from anti-racist struggles in recent years partly because of their white "guilt". The appalling quarrels in 1995 between the Anti-Nazi league and the Anti-Racist Alliance in this country is a perfect example of this. In the United States there is no room for even basic conversations. Saul Bellow spoke movingly about this last year. He was accused of racist stereotyping in his novels. Since then there has been no space for him to discuss this because, he says, there is no vocabulary for such encounters.
Patricia Williams believes this is completely unacceptable. She deplores separatism. In fact she has been a vociferous critic of black neo-nationalists such as Farakkhan. She will not even support reparations movements: "What I am talking about is an inclusive ethical project which takes seriously economically dispossessed white men as well as minorities; a broad national movement where we develop a civic responsibility toward one another. Black and white fates are tied together intricately. I remember that James Baldwin spoke in these terms when said that conscious blacks and whites needed, `like lovers', to work together to end the racial nightmare. As did Martin Luther King, just before he was shot. And Bill Clinton, on his inauguration day, also asked: `The divide of race [is] the nation's constant curse. Will we be one nation or will we fall apart?'" Patricia Williams is with worthy friends on this missionn
The Reith Lectures begin on 25 February on Radio 4, at 8pm.