Mr Galbraith had accepted the recommendation of the Riddell committee in 1999 that the pound;12 million grant from the Scottish Executive should be distributed among the education authorities, arguing that the schools draw pupils from their local areas.
But a campaign by the schools, led politically by Brian Monteith, the Tories' education spokesman, provoked a series of tentative moves from ministers culminating in last Friday's reprieve, which maintains direct funding until 2008.
The original decision was to have taken effect in 2001, later postponed until the following year. After a meeting with the schools two years ago Nicol Stephen, Deputy Education Minister, announced there would be no funding change until March this year.
Mr Stephen then embarked on a series of visits to the seven schools concerned - Donaldson's College for the Deaf in Edinburgh, the Royal Blind School in Edinburgh, Corseford School in Kilbarchan, Craighalbert School for cerebral palsy in Cumbernauld, East Park Home in Glasgow, Harmeny School in Balerno and Stanmore House in Lanark.
During a debate on the parliamentary education committee's report on special needs in May 2001, Mr Stephen appeared to concede the arguments of the schools' supporters. He acknowledged the importance of national specialist provision and said the seven centres could make a reality of mainstreaming special needs youngsters in schools, particularly in rural areas, by offering expertise, research and outreach work.
Mr Monteith, commenting on the latest decision, said: "The Scottish Conservatives have consistently argued that grant-aided status for these specialist schools is vital for their continued existence.
"Had funding been diverted to local authorities, it is highly likely that, due to a combination of financial restraints and ideological dogma, the existing excellent provision would not have been funded. This would have had highly damaging consequences for these children's education."
While the Tories hailed a U-turn, Ms Jamieson's letter to the schools portrayed it differently. It stated that the decision was based on the fact that substantial legislative and other changes which have occurred in special education should be allowed time to bed in.
"When we have had the opportunity to make a proper assessment of the effect of these radical changes," the letter continues, "we will be in a better position to reach a judgment on the role, if any, which the system of direct grant aid will have in the future delivery of specialist education.
"Accordingly, at the present time, I do not anticipate that the issue of reallocation (of funds from the Executive to local authorities) will be revisited until 2008 at the earliest."
Lillemor Jernqvist, director of the Craighalbert Centre, welcomed the decision which she said would give the school a secure future, allowing it in particular to expand its outreach work.