ERA member Tania Tetitaha declined Mr Rudd's application and said Rudd had used his fame to promote Phil's Place and his involvement with the restaurant was well known. She said the ERA understood Rudd had been "intimately involved" with the cause of the dispute.
Allegations against Rudd's restaurant were lodged in August 2012, but details of what is alleged are yet to be revealed.
He was not a "passive bystander" and the ERA understood "he does not largely dispute what occurred and his involvement".
"If [that is] so, his reputation cannot be marred by events he accepts are truthful," Ms Tetitaha said.
"There are no exceptional circumstances or real risk to the administration of justice if this evidence were published."
Media had also already published his connection with the dispute, rendering any name suppression useless, she said.
Rudd has owned Phil's Place since 2011. The restaurant closed last July but re-opened and a new management structure was brought in on April 13.
Rudd left AC/DC in 1983 and retired to New Zealand but rejoined the band in 1994.