The judge ruled that, according to the law set down in the 1800s, it was essential for a conviction that the woman was subjected to some degree of force or threat of force.
Mr Watt, 23, was duly acquitted, despite the fact that the woman had repeatedly said no.
After the judgment, Colin Boyd, the then lord advocate, asked the Court of Criminal Appeal to review the definition. A panel of seven appeal judges, including Lord Cullen, the then lord president, issued a decision that agreed with Mr Boyd's submission that a man could be convicted, even if he does not use force to overcome a woman's will.
Rape in Scots law was thus redefined as penetration without consent. The move was praised. But this ruling threw up further problems,which led to a review of the law on rape and new legislation in 2009.
Despite the commissions and reviews and recurring work of different lord advocates to improve the way rape cases are prosecuted, Scotland still has an abysmally low conviction rate, with just 3% of all cases reported to the police resulting in a successful conviction.
That is why, in part the Crown Office and Scottish Government wish to abolish corroboration.
At the time Mr Watt was a final-year law student at Aberdeen University. He insisted the woman was a willing partner and he was cleared of all charges as he had committed no crime as the law then stood.
Scotland's most senior law officer praised the "courage and dignity" of the woman whose case led to a tightening of the rape laws.
Mr Boyd, the then Lord Advocate who is now Lord Boyd, said: "The position of complainers in rape cases is often difficult, but she has shown great courage and dignity throughout this lengthy legal process."
"I remember the judge saying he was acquitted," says Mary Ann Davison, speaking out for the first time. "I burst into tears. Before then I didn't really understand the term bursting into tears, it is the only time that I have ever done it. The judge seemed to say that no meaning no did not apply."
Before the trial Mrs Davison took a year out of university, in part to avoid bumping into Mr Watt.
"The person I accused was a neighbour," she said. "He was a year ahead of me so I hoped he would have graduated and gone by the time I got back.
"It was a year spent waiting for the trial. I still remember giving evidence and how it felt. The defence said there was no case to answer. I remember sitting there over lunchtime. It was an hour or two before we were called back.
"I was taken away to a room and the prosecutor came in and said how sorry he was. The next day it was in all the newspapers and I started to get a sense of the scale of the implications.
"I remember buying the papers and thinking this is about me, but in a way I had contributed nothing to it. It was such a strange feeling. I remember too when Mr Watt said he would sue me for defamation of character."
Mr Watt never carried out his threat to sue, but became a hate figure with women's groups for his comments. She says her story has worked out better than she imagined it would more than a decade ago, but now she wants to be able to help other women.
"I got a 2:1 for my history degree," she said. "I wanted to use the history part of my degree and I got a job at Oxford University as an archives assistant. Then I went on to do a Masters in Archives and Records Management.
"I am nervous about speaking about this. It's not easy, but I think the removal of corroboration is important."