Professor Alan Rodger, who helped transform the Beatson West of Scotland Cancer Centre into one of the best facilities of its kind, also launched a scathing attack on the SNP's health record.
The former oncologist said Nicola Sturgeon and her successor as health secretary Alex Neil were more interested in hiding bad news and attacking critics than improving the service, and said the Yes camp had hypocritically adopted the scaremongering tactics it has repeatedly accused the No side of using.
In England, private companies can bid to run NHS services and the Yes campaign has said that while health policy is devolved to Scotland, cuts to NHS funding south of the border as a result of privatisation, patient charging or austerity would have a knock-on impact and see Scotland's budget slashed, under current arrangements.
But Prof Rodger, who retired in 2008 and backs a No vote, described the claim as far fetched and said that Scotland's health statistics had remained worse than those in England.
He added: "It seems to me that the pro-independence [side] has hypocritically decided to adopt the strategy it has accused the No camp of following by deliberately spreading fear about the NHS and its future.
"Meantime the SNP government which has been in charge of guiding the Scottish NHS for over seven years continues to fail in its duty yet has the gumption to say that the Scottish NHS would be in danger if there is a Yes vote."
Prof Rodger attacked Scottish breast cancer surgeon Dr Philippa Whitford, who warned Scotland's NHS would wither away within a decade without a Yes vote, pointing out that the health service in Scotland also sends patients into the private sector.
He added: "That devolved government has been left to decide how to spend its money on health, education, transport, law and order - and future devolved governments will continue to do so if we sensibly vote no."
Prof Rodger, who spent 11 years in Australia before returning to Scotland to work at the Beatson, spoke out after Dr Anna Gregor, who led the country's successful cancer strategy and was recognised for her services to medicine with a CBE, said fellow doctors and politicians had told a "total and utter lie" by saying Scotland must become independent to protect the Scottish NHS.
However, the Scottish Government defended its record, saying its decisions had meant the NHS north of the border was a world leading organisation, and maintained that the NHS would be better protected in an independent Scotland.
A spokesman added: "Our NHS has brought levels of C. Diff to the lowest on record, has seen patient satisfaction continue to rise, has dramatically cut patient waiting times and has continued to increase the number of healthcare workers.
"Under current arrangements, any cuts to the health budget in England through austerity, privatisation or patient charging will have a knock-on effect which cuts Scotland's budget.
"That is one of the reasons why the Scottish Government believes that our health service would be better protected under independence.
"We are committed to protecting the founding principles of the NHS and maintaining it as a publicly-owned health service, free for everyone at the point of use. We believe that there should be constitutional protection for the NHS in an independent Scotland - which would ensure that the NHS will be in public hands for generations to come."