The refusal followed a demand for disclosure from Academics Together, an offshoot of the pro-Union Better Together campaign, which said that if the SNP was wrong it would mean a black hole of at least £150 million in university budgets.
Unlike students south of the Border, who face fees of up to £9000 a year, Scottish residents receive free university education if studying in Scotland.
Students from EU countries outside the UK cannot be charged fees to study in Scotland as it would be discrimination on the grounds of nationality, meaning they also receive free tuition.
However, Scottish universities can and do charge fees of up to £9000 a year to students from England, Wales and Northern Ireland, as the EU allows differential regimes within the UK.
Anxious to avoid a rush of rUK "fee refugees" swamping Scottish universities, the SNP say that if Scotland was independent, its universities would still be able to charge students from the rest of the UK (rUK), even though the rUK would be a separate EU state and could not normally be discriminated against.
The White Paper claims Scotland could justify an opt-out because of the UK's relative size, the different fee levels, shared language and borders, and the high demand for places.
One option for ministers would be to insist on rUK students becoming Scottish residents before they got free education, but this is not a demand currently imposed on other EU citizens.
Academics Together, which publishes a report on the subject tomorrow, said an independent Scotland would "run into significant problems with EU law" and that if rUK students no longer had to pay tuition fees, even if their numbers stayed the same at around 5000 a year, it would cost universities £150m a year.
Paul Beaumont, professor of European law at the University of Aberdeen, said: "It is hard to see the Court of Justice of the EU accepting the Scottish Government's arguments as to how this overt discrimination against students from rUK can be justified. There is therefore a substantial hole in the Scottish Government's plan for funding higher education in Scotland."
And Niamh Nic Shuibhne, professor of European Union law at Edinburgh University, said the Scottish Government would face "an extremely steep uphill battle" to convince the EU that it should be allowed to discriminate against rUK students.
Earlier this year, umbrella group Universities Scotland published preliminary legal advice which said it "may" be possible for an independent Scotland to charge rUK students on residency grounds.
However, it added that ministers would need to show the step was "necessary" and "appropriate" to achieve a "legitimate" aim, such as averting the collapse of the free tuition policy, and that more analysis was required.
Other EU countries have failed to convince the EU court on similar points in the past.
Academics Together spokeswoman Professor Susan Shaw, former vice-principal of Strathclyde University, said: "All the evidence points to the fact that Alex Salmond's assertions on tuition fees don't stand up to scrutiny."
A spokesman for Education Secretary Michael Russell said the White Paper was consistent with legal advice received by the Government, but it was a longstanding convention of both Scottish and UK Governments not to publish such advice other than in exceptional circumstances.
He added: "There is, however, very clear legal opinion already published by the universities themselves on this issue.
"It makes clear the possibility of continuing the current system within EU law."
He said it was "nonsense" for the No campaign to ignore this advice to Universities Scotland.
"Instead they are trying to generate a scare story from Academics Together - every one of whom is signed up to the No campaign and putting forward arguments against Scottish independence. When the universities themselves acknowledge that there is a good basis for this policy, the No camp should quit their self-styled Project Fear approach."