The investment made Rinehart the largest shareholder in the company, which publishes the Dominion Post and other newspapers in New Zealand and the Age, the Sydney Morning Herald and the Australian Financial Review in Australia, as well as owning a string of radio stations.
Fairfax is one of the media groups that has opposed Rinehart's bid to keep secret the family litigation over the trust deed.
Her children Hope Rinehart Welker, John Langley Hancock and Bianca Hope Rinehart have taken NSW Supreme Court action against Rinehart, the only child of the late mining magnate Lang Hancock.
They want to oust her as trustee of the multibillion-dollar family trust, set up by Hancock before he died, of which they are beneficiaries.
Her other daughter, Ginia Hope Frances Rinehart, is supporting her mother, who has been successful - to date - in keeping all details of the dispute secret.
Late on Wednesday night, in an urgent application to the High Court, she obtained an extension on suppression orders until March 9.
On that date, she will apply for leave to challenge a NSW Court of Appeal ruling which revoked the suppression orders.
Rinehart went back to the Supreme Court on Thursday with a new application claiming publicity about the deed dispute would endanger her, her children and her grandchildren.
But Justice Michael Ball concluded the orders were not necessary to protect their safety.
He refused to suppress the material filed to support her fears for safety claim, which led to the widespread publicity on the emails and the security report.
Codenamed Project Tara, it cited case studies "where media profiles have been a factor in attracting high risk or actual threats".
Examples included English footballer David Beckham, American comedian David Letterman and Sydney fake collar-bomb victim, schoolgirl Madeleine Pulver.
In his affidavit, Rinehart's lawyer referred to her safety fears "arising from the worldwide media coverage of her wealth and the intense media coverage of proceedings". He listed examples of derogatory comments posted on social media sites since the court action began last September.
- AAP