His comments to journalists that councils were keen to end selective admissions had prompted headlines that Labour was "itching to axe the grammars", which were accompanied by a terse "Graham Lane speaks only for himself" from a spokesman for Labour education spokesman David Blunkett.
And while Mr Lane, chairman of the CLEA, may have taken momentary pleasure from his dig at the Daily Mail he should perhaps focus the attention of the Labour leadership on the thinking in local authorities.
For it is clear now that local government, which just a short while ago was being written off, has a future under a Government of either of the two main political parties.
Mr Blunkett opened last week's CLEA conference in Solihull with a roll-call of praise for councils, the bulk of which are now Labour-controlled. And Robin Squire, schools minister, closed it by saying that LEAs had a significant role to play - but that they should not be in the business of controlling or running schools other that in the most exceptional circumstances.
He added that any role that included planning school places and setting up the education budget had to be significant.
"LEAs can be a powerful force for good," Mr Squire told the conference. "But realising that potential will require continuing development of assumptions, attitudes and practices."
The ultimate aim for government was higher standards - through self-government by schools not imposed from outside. "It must grow from within."
Local authorities were there, he said, to do the things that schools could not do themselves, and that no other agency was better placed to do.
During the past 17 years the role of the local authority has changed almost beyond recognition. More powers have come under the Secretary of State's control but others have been devolved to schools and governing bodies.
Councils now face serious difficulties over budgets and the CLEA is seeking assurances from Education and Employment Secretary Gillian Shephard that future levels of funding will be increased to reflect their true levels of spending.
They have already told her they need an extra Pounds 1 billion next year and armed her with the evidence to fight their case with Chancellor Kenneth Clarke.
Many also fear that the Government proposal to make them delegate 95 per cent of budgets to schools will leave little or no room to manoeuvre.
According to David Blunkett, Labour is already making a difference in local government. "Think how much more of a difference could be made with central and local government pulling in the same direction," he told the CLEA.
They would not appear to be pulling in the same direction on grammar schools, in public at least. Tony Blair has said the country's 161 grammar schools would only be abolished under a Labour government if a referendum of parents voted in favour. Privately things may be different.
Mr Lane, for his part, insists that all he is talking about is party policy. He says that under a Labour Government there will be moves to reform admissions policies and to phase out grammar schools where they already exist.
One suspects that the plea from David Blunkett to the CLEA for councils to put aside "petty squabbles" of LEA versus grant-maintained schools may lead to similar differences.
Many of those squabbles are far from petty and there will be local authorities who will be unable to resist putting the boot in if a Labour government is elected.