Austereo on Tuesday was granted permission to appear at Ms Saldanha's full inquest scheduled for May 2.
Lawyer Maya Sikand argued because of the station's "perceived involvement" with the nurse's death it should be able to examine witnesses "where appropriate".
Ms Sikand noted her client had apologised for any "unforeseen and totally unintended consequences of the call".
Ms Saldanha's husband Benedict Barboza and teenage children Junal and Lisha were at Westminster Coroner's Court for the hearing.
Family lawyer John Cooper QC flagged a dispute over whether Austereo called the hospital prior to broadcasting the prank call as the station has claimed.
"As far as we are aware no such contact was made," Mr Cooper told the court.
The family is also upset Ms Saldanha was answering calls at the matron's office.
"Was it within her contract of employment and capabilities?" Mr Cooper asked, adding whether Ms Saldanha received proper care and counselling afterwards was beside the point.
The May inquest will hear evidence from the duty nurse who gave the Australian DJs details of the Duchess of Cambridge's medical condition.
But she won't be identified in any news reports.
Hospital lawyer Fiona Barton QC on Tuesday argued the "facts cry out for anonymity" to ensure the duty nurse didn't feel the same scrutiny as Ms Saldanha.
Coroner Fiona Wilcox agreed.
She plans to review the deceased nurse's contract and the hospital's confidential security policy before the inquest.
Other witnesses scheduled to give evidence include the colleague and security officer who found Ms Saldanha's body at staff quarters near the hospital.
King Edward VII chief executive John Lofthouse will appear alongside the lead police investigator.
The matron in charge at the time could also be called to help examine Ms Saldanha's state of mind after the hoax call.
British MP Keith Vaz spoke to reporters outside the court flanked by the nurse's family.
"Today marks the beginning of the end as far the legal process is concerned but it does not take away the terrible grief the family are still suffering," Mr Vaz said.
"The next few weeks are going to be very difficult for the family until May 2 when, of course, the inquest will begin."
- AAP
