Ring-fencing of education funding has offered schools some guarantee that the priority given by the Scottish Government to education will be reflected in school budgets. Removing ring-fencing opens up the prospect that the money allocated to education will be spent by local authorities on other services. Already, the proportion of national education funding that reaches school budgets is clouded in the arcane mysteries of local government finance.
What is certain is that the proportion is unacceptably low - far too much is spent centrally by the councils. These changes to funding are being imposed against a background of ever-greater demands on resources as a result of the Government's laudable commitment to reducing class sizes.
Ms Hyslop's message that the SNP Government will not micro-manage schools received a lukewarm reception from heads and deputes who are more concerned about the prospect of an increase in micro-management by authorities. The Scottish Government has never micro-managed schools, which are more under the control of local authorities than those in England or Wales.
In all three countries, the question is whether the value added by the authorities represents good value for money for the schools and the taxpayer. In Scotland, that question will be of increasing importance after the removal of ring-fencing.
Will local authorities, for example, pluck up courage and support heads by sacking incompetent teachers? If they don't, they should give the power to the heads - and support them when they take action.
Will education authorities put into action Ms Hyslop's declared wish in her HAS conference speech that school leadership teams should look different in the future, making the most of the opportunity to bring on young leadership talent as the post-war baby boomers come up to retirement in record numbers in the next three years?
Will authorities introduce more flexibility into school staffing structures, so that schools can design their management structures to match their particular needs?
Unless they delegate more power to individual schools, the answers will be negative.
With five million people, Scotland does not need 32 local authorities - any more than Wales needs 22 for its three million population. The heads want a national framework for the education service, with flexibility - but the flexibility needs to be at school level, not in council offices.
Where councils have a role to play - as HAS retiring president Charlie McAteer said in his speech to the conference - is in strategic planning and in the provision of responsive and joined-up local services, so that children in trouble can be supported without the delays and bureaucracy that so often characterise existing arrangements.
School leaders must have the management flexibility they need to raise achievement and increase opportunities for young people in a sustainable way. This means that central government has to provide the policy framework and the funding local government needs to provide support for the schools and school leaders to be empowered to improve the standards of teaching and learning.
Ms Hyslop spoke of creating a "new relationship with local authorities". What is really needed is a new relationship with schools.
John Dunford is general secretary of the Association of School and College Leaders in England and Wales.