In early July, Mr O'Byrne resigned as the leader of the Tasmanian Labor Party - less than a month after securing the position - in the face of allegations of sexual harassment.

His statement then was extraordinary.

Rather than following the supposed political advice of Winston Churchill of "never apologise, never explain", Mr O'Byrne appears to have made substantial admissions along with expressing contrition.

"I acknowledge that my behaviour did not meet the standards I would expect of myself," he wrote. "I also acknowledge that I have let down my wife and family."

He went on to explain that "at the time ... I genuinely believed the kiss and text exchanges to be consensual", but "now understand that this was not the case."

Saying he had written to the woman - who, at the time, was a 22-year-old employee of the union of which Mr O'Byrne was the secretary, and, therefore, her boss - to "offer my unreserved apology", he also "genuinely" thanked her for "having the strength to bring this issue to light".

How his tune has changed after Labor's independent investigation into matter.

The party would only say on Tuesday that former Fair Work Commissioner Barbara Deegan had determined that no further action should be taken.

Labor refuses to release the full report, nor say much, if anything, of the detail of its findings, while there have been concerns expressed that some witnesses were not given the chance to provide evidence.

In another statement, however, Mr O'Byrne said: "The Deegan Report has found that I did not engage in any sexual harassment or victimisation of the complainant."

As far as the Franklin Labor MP is concerned, the matter is over, and he's focused on redoubling "my efforts to support the Tasmanian Labor Party and to hold the Gutwein government to account".

Clearly, he's determined to continue his career in politics, but whether he can - or should - really rests on one question that will not go away anytime soon: How is it possible to reconcile his two statements?