Gina Rinehart has been the subject of ''unflattering'' and ''threatening'' media reports and the safety risk to the iron ore magnate, her children and grandchildren would escalate should details of the family's feud be made public, a court has heard.

Mrs Rinehart, Australia's richest woman, is attempting to obtain a suppression order over the ''serious misconduct'' she is alleged to have engaged in as trustee of the family's multi-billion dollar trust.

Documents tendered to the NSW Supreme Court yesterday contained an email sent by Mrs Rinehart to Michael Stutchbury, the editor of The Australian Financial Review, complaining about a graph published in the newspaper illustrating Hancock Prospecting's royalty income projections.

Mrs Rinehart opens the email with ''From over exposed!''

She then writes, ''I haven't read all the media, there's too much of it!, and I get tired of reading about 'me' (don't others?)''.

Matthew Walton, SC, for Mrs Rinehart said if the High Court refused to grant special leave to appeal, the stay on the lifting of suppression orders in force would come to an end and ''we will need protection''.

Mr Walton said three of Mrs Rinehart's children - John Langley Hancock, Bianca Hope Rinehart and Hope Rinehart Welker - were seeking to replace her as trustee.

''The plaintiffs would come to control the assets of the trust … that in itself is good reason not to release any information concerning the particular financial circumstances of the trust and the prospects of the plantiffs,'' Mr Walton said.

Mrs Rinehart's lawyers submitted two security risk assessments prepared by ex-Australian Army officers as evidence of the increased risk of kidnapping for ransom that further media reporting would allegedly cause.

Justin Bowden, formerly an officer of the Royal Australian Corps of Military Police, described historic cases of kidnapping affecting wealthy families, including US newspaper tycoon William Randolph Hearst, whose granddaughter Patricia was kidnapped by the Symbionese Liberation Army, and oil tycoon John Paul Getty, whose grandson John was held hostage by a gang of criminals.

Anthony Moorhouse, a former counter-terrorism commander in the special forces, said if the suppression order was lifted, ''Mrs Rinehart will be required to expend considerable additional resources on increasing the safety and security precautions for herself, her family and her assets. This will undoubtedly cause not only a financial but lifestyle burden to the family.''

But David Thomas, for the three eldest children, said the expert reports did not make a link between the lifting of suppression orders, media attention and increased safety risk.

''It's not enough to say that a particular person suffers from unwanted media attention and then to say but for a suppression order that unwanted attention will increase, ergo, a suppression order is needed,'' he said.

The court also heard Mrs Rinehart's insurance company had threatened to withdraw the ''ransom insurance'' policy she held for her family after its existence became public. The insurance company eventually offered to renew the policy, but doubled the premium, and will only agree to cover Mrs Rinehart, her daughter and ally Ginia, 25, and her grandchildren.