Lawyers produced a security risk assessment warning that Rinehart and her children would be placed at risk from "criminals and deranged persons" if case details were published.
The court found suppression of the documents was not necessary to protect their safety, allowing international publication of correspondence including emails begging money to pay for bodyguards and household staff.
The order will be argued again in the High Court on March 9.
Yesterday Fairfax newspapers reported that Rinehart had threatened to withdraw the ransom insurance policy taken out to protect her three oldest children if their lawyers did not reverse their opposition to the suppression order before a NSW Supreme Court duty judge.
The Sydney Morning Herald quoted a letter from Rinehart's lawyer to their counsel, concluding that the children's failure to support her application for suppression indicated they were no longer worried about their security.
"We can only presume that your clients' previously stated concerns for the personal safety of their families and themselves have now completely and entirely disappeared," Paul McCann, a partner at Corrs Chambers Westgarth, said in the letter cited by the SMH. "Under these circumstances, it seems your clients would place no value in the continuation of 'ransom insurance' that is currently provided to them and/or their young children.
"Our client has been reluctant to discontinue the relevant insurance policies [but] given your clients' about-turn ... our client is now exposed to attack by your clients if she continues this insurance for them."