Hayton last night rejected the claims and defended his organisation's leadership style.
"In the eight years I was at the NZRL there was never a culture where we would celebrate being beaten by the Australians," said Guttenbeil.
"When touring with the Kiwis, we always had legends like Ruben Wiki who would take the boys back to the team hotel to have a few drinks, some kava, and reflect, and if you lost, not go anywhere, so something has obviously changed.
"Everything starts from the top.
"When you have a strong board, a strong chief executive, it does create a different culture.
"I don't know that the senior leadership group at the NZRL have the mana to imprint a recipe for success anymore. It is then left to the senior players and a couple of managers to try and do that on tour, which is a pretty hard ask."
Under former NZRL chief executive Jim Doyle and former head coach Stephen Kearney, Guttenbeil and Tamati worked to reinforce protocols and guidelines to ensure high standards of discipline and accountability.
Guttenbeil is not sold on the Kiwis Te Iwi Kiwi culture, which was initially implemented by Kearney following the failed 2013 World Cup campaign, with an overall message of selflessness and shared commitment to the team's values and goals.
Under those ethos, Guttenbeil believes too much weight has been given to the players' senior leadership group with little direction coming from above.
"Traditionally the Kiwis have always been more a representation of the whole of New Zealand," he said.
"The culture of the Kiwis is now they are this tribe among themselves."
Tamati, now general manager for the NRL Auckland Nines, believes the NZRL management failed to ensure players were kept on a tight leash.
"If your leaders aren't leading by embracing those values, you can't expect anybody else to," said Tamati.
"David's job is to coach the team and that's what he's measured on or against but everything else comes from management from within NZRL.
"They are the management, they are the leadership team, they are the ones who should be questioned on why this is happening."
Tamati's work with the Kiwis proved invaluable to her efforts to ensure there were no reported off-field incidents while hosting 288 NRL players in Auckland for the Nines over each of the past four years.
"You wrap a whole integrity plan around keeping everybody safe and out of trouble and no incidents in four years doesn't just happen, it happens because of the massive effort," Tamati said.
"You don't just go 'Oh they can take care of themselves', you put massive policies around them.
"There are rules and they are all clear about what they are."