Health secretary Alan Milburn was forced to intervene after a blunder by NHS chief executive Nigel Crisp during the conference.
Answering journalists' questions after his keynote speech, Mr Crisp refused to rule out the prospect of private consultants bidding for 'franchises' to run strategic health authorities and failing trusts.
'We want to free up people's thinking about it, 'Mr Crisp said.
'When people are saying they are willing or interested in taking over this service, they will provide a business plan. The trust chair will accept a plan for somebody to come in and run that particular organisation.'
The 'organisational structure behind that' did not really matter.
'They could be self-employed, ' he confirmed.
And when asked if an ex-NHS manager working as a private consultant could bid, Mr Crisp said 'if he comes in through the sort of process where We have accredited people', this would be possible.
The new process would 'create a degree of contestability', Mr Crisp said, but he was not expecting bids from major private companies.
Mr Milburn was forced to contradict his chief executive, after confederation chief executive Stephen Thornton warned that the franchise scheme as outlined by Mr Crisp could fall foul of tendering law.
Mr Thornton had called for 'urgent clarification' of the franchising scheme. 'Is this keeping it within the NHS or is it privatising it?'He added that if the scheme extended beyond the 'NHSemployed managers' to people 'putting in a bid on their own' or ex-NHS managers, 'it seems to me That is the point at which you fall foul of the tendering rules'.
A bidding process would mean private companies would have the legal right to get involved, he said.
'The franchise would have to go through the EU tendering rules.'
Within the hour, Mr Thornton said he had received reassurances from ministers that 'topperforming trusts' would 'be able to compete to run failing trusts, but this will remain entirely within the NHS family' and that the leadership of such teams would come 'entirely from within the NHS'.
Rumours that Mr Crisp's gaffe had angered the health secretary were reinforced by an apparent snub at a conference dinner, when Mr Milburn greeted Mr Thornton effusively, but failed to greet Mr Crisp.
But on Friday, Mr Milburn told HSJ : 'Nigel and I have exactly the same position. It is going to be led by NHS managers. Franchises are about NHS managers and NHS clinicians.'
Earlier, Mr Crisp said the franchising scheme would give NHS managers career opportunities, and help trusts in 'keeping the best people'. Teams of NHS managers would be able to bid to run failing trusts, while applicants to run the strategic HAs would be asked: 'Do you want to do so on a franchise basis ? Will you bring your team?'
Asked whether the extra resources he was offering for management teams to run failing trusts would go to the individuals or to NHS managers' employer trusts, Mr Crisp said 'probably both'.