But the notes say she lacked confidence - "as with other comprehensive school pupils".
Laura, from Monkseaton Community High School in Whitley Bay, Tyne and Wear, went on to gain a place studying biochemistry at Harvard University in the US.
However, Dr Lalvani ended his notes by saying she would make an "excellent" doctor.
The revelation of his comments - obtained exclusively by the BBC - appeared to go to the heart of the row between Oxford and the government over admissions of state school pupils.
Click here to read the full note
After the university refused Laura, 18, she became one of only 10 British students to win Harvard scholarships - worth, in her case, £65,000.
She gained 10 A* GCSE exam passes, and is expected to do equally well in her A-level exams.
Education minister Malcolm Wicks told Radio 4's The World at One programme the interview notes were "telling".
"If that kind of stupid comment is being made about comprehensive school children, lacking confidence, then that says more about those making the judgements than about extremely able people being brought up in our comprehensive school system," he said.
But Dr Lalvani gave a different interpretation, in a statement issued by the university.
Compensating
"Like several of the other comprehensive school students we interviewed that day, Laura appeared slightly unconfident," he said.
"We were at pains not to let this disadvantage her in any way.
"The aim of the remark ... was to ensure that we compensated as far as possible for any disadvantage there might have been for her state school background.
"There was no suggestion intended that all state school candidates are less confident than private school candidates," he said.
Earlier, Oxford's vice-chancellor, Dr Colin Lucas, criticised the Chancellor of the Exchequer Gordon Brown for stoking up the row on Thursday.
Mr Brown said it was "an absolute scandal" that a pupil from a state comprehensive had been refused a place at an Oxford College - only to win a scholarship to Harvard.
Dr Lucas said Mr Brown had been speaking without being in full possession of the facts.
He did not think the university had "anything to be ashamed of".
'Elitist'
Dr Lucas added that the university had the smallest medical school in the country, with 113 places for this year.
"Almost twice as many women have been offered places as men for this coming year, and almost exactly the same numbers of places have been offered to state schools and independent schools," he said.
Admissions trend
"As far as the north of England is concerned, we are taking 63% of people from the state sector as distinct from the independent sector, so I don't think this is a scandal in the terms which are suggested."
He said the statistics which should be considered were those showing the percentage of people who achieved three grade As at A-level.
The Department for Education says 56% of those students last year were from state schools, 44% from the independent sector.
Of Oxford applicants, 56% were from state schools.
"For this coming October, 53% of our offers have gone to applicants from the state sector," Dr Lucas said.
"But five years ago, 47% only were receiving offers from us. So in five years we have reversed the trend, and we are moving."
Oxford University Students' Union has complained of a "cynically minded attempt by Gordon Brown and the government to jump on a populist bandwagon".
It said it was devoting a lot of effort to countering the image of Oxford as an institution which favoured those from more privileged backgrounds.
"Spence: A sense that this is an outstandingly intelligent young woman. She has a certain poise, and appeared very thoughtful, sensitive and perceptive. Also highly motivated (OU [Open University] maths A-level on her own steam). Musically talented. As with other comprehensive school pupils, low in confidence and difficult to draw her out of herself despite being able to manifestly think on her feet. Will be an excellent doctor."
Dr Lalvani, who made the notes, is one of the six academics involved in the medical admissions process at Magdalen College.