At today's hearing Judge Grant Fraser said Mr Rush's concerns about the right to a fair trial were no longer relevant and rejected the application for permanent suppression.
"There are no compelling reasons or very special circumstances in this case that justify the departure from open justice.''
Mr Rush faced a three-day trial last month which ended with the jurors finding him not guilty of injuring with intent to injure and assault.
He had been accused of attacking 70-year-old Neil Slater outside Mr Rush's Auckland home after an argument about parking.
Mr Rush's wife Larissa Rush told the court she saw Mr Slater kick and punch her husband while her husband knelt down to fit a wheel clamp to Mr Slater's van. Mr Slater denied this.
Mr Rush's company, Darien Rush Security, previously held the security contract for Eden Park, including during last year's Rugby World Cup.