Speaking at Holyrood, the First Minister said an independent investigation into care at the mother and baby unit (MBU) at St John's Hospital in Livingston had found no evidence to support allegations the service was "dangerous, unsafe or dysfunctional."
Last night, however, Mr Salmond's position was challenged by the doctor in question, as well as the family of a former patient who committed suicide who are suing NHS Lothian for medical negligence.
Mr Salmond was answering a constituency question from Neil Findlay, the West Lothian MSP who is also Labour's health spokesman.
He had asked whether the First Minister would intervene after The Herald revealed Dr Jane Hamilton, a consultant psychiatrist, had refused to sign a severance agreement with NHS Lothian amid fears it would gag her.
Dr Hamilton spoke out yesterday for the first time even though by doing so she risks losing a six-figure settlement and possibly the sack.
Mr Salmond told MSPs that an independent investigation into the unit in question was undertaken by Dr Margaret Oates, the consultant psychiatrist at Nottinghamshire Healthcare NHS Trust, and it reported in 2012.
Mr Salmond said: "The independent investigation was undertaken by a consultant physician of high standing outwith the Scottish NHS."
However, Dr Hamilton said: "That inquiry did not address the issues I raised. I warned the health board and the health minister of this before it even began its work.
"I also expressed serious reservations about the choice of Margaret Oates because of her earlier frequent visits to the MBU on behalf of the peer review network she chaired, when she had found no great problems."
A briefing note obtained from the Scottish Government under freedom of information legislation confirmed ministers were warned about Dr Hamilton's concerns over "the impartiality of the upcoming external review into these issues."
A later document said the inquiry was "carried out by colleagues for the most part already known to management and to the service team."
The father of Claire Donald, who jumped off Erskine Bridge three years ago, also questioned the independence of the inquiry.
Jim Waggitt said: "Margaret Oates headed the inquiry into our daughter Claire's death. She said to us in front of witnesses 'had your daughter received the proper care and monitoring, she would have got better'.
"She said it would have taken up to a year, but Clare would have got better ... I remember that. So does my wife and my son-in-law and his mother. But that wasn't the conclusion of her report.
"Then she was the one who NHS Lothian chose to head the so-called external inquiry into the issues that Dr Hamilton apparently had raised. Dr Oates wasn't exactly a stranger to the MBU."
Neither Mr Waggitt nor Dr Hamilton question the professional competence of Dr Oates but believe NHS Lothian choosing her had not made for a genuinely external review.
However, Mr Salmond did say that Health Secretary Alex Neil would check again to ensure that Dr Hamilton was not being gagged.
NHS Lothian insists it was not trying to gag Dr Hamilton and that her right to be a whistle-blower was specifically safeguarded.
Dr David Farquharson Medical Director said: "The confidentiality statement confirms that, for the avoidance of doubt, Dr Hamilton will not be prevented from making a 'protected disclosure'."
But Dr Hamilton said that her legal advisers had studied the document in question and had advised her that the health board's classification of her clinical concerns as employment grievances which had to be withdrawn did indeed represent gagging.
Dr Kim Holt, the whistle-blowing consultant who was suspended then vindicated after the death of Baby P in London in 2007, has written to Alex Neil in support of Dr Hamilton.
The Herald tried to contact Dr Oates without success.