The New Zealand Cricket board met for a scheduled meeting in Wellington on Monday and spent five hours discussing the captaincy debacle, which included meeting Hesson.
"No heads are going to roll,'' Moller said. "There were no hanging offences in all of this. Yeah, the ball's been dropped, absolutely. Could we have done things better? Absolutely. Are we going to learn from those mistakes? Well we hope so. Is there any reason for anybody to have their heads taken off? No, and that is a decision the board has made.''
Taylor said in a radio interview earlier this week that someone within NZC was "definitely'' lying with regards to how the situation had been portrayed.
As for the "additional material'' that has been uncovered, Moller said it was being investigated but couldn't talk specifics and couldn't offer a timeframe for when the matter would be resolved.
"We are on the case, but ... I'm not going to put an arbitrary deadline [on it]. We will move forward as quickly as we can but we do these things - although the events of the last week may not evidence this - we'd like to think we do these things in a considered, sensible and well-thought-out manner.''
There were numerous points discussed at today's press conference, but one of the key messages was that New Zealand Cricket's board will be given a shake up, potentially by the end of the summer.
Following the recommendation of Sport New Zealand, NZC engaged the services of Boardworks International to conduct an independent review last year.
The 39 recommendations in that report were released to the media in September this year and since then the NZC board has consulted its members about the recommendations.
Two of the more important recommendations were that the current elected board of eight should be changed to six elected and two appointed positions and that elected members and appointed directors should be able to self-apply rather than require a nomination by the members as is the status quo.
That system is commonplace among most sporting bodies in New Zealand and Cricket Australia also uses that approach. A special general meeting next year will look to adopt a more modern constitution for the NZC board.
Moller didn't want to put a specific time on when the special general meeting would take place but said he hoped it would be by the end of the summer and he urged more former players to put their hands up to join the board.
White also pointed out that Martin Crowe resigned from his post as a talent scout with New Zealand Cricket on November 30, before the captaincy situation played out in the media.
