Christian said that their call to London's King Edward VII Hospital -- which was treating Prince William's pregnant wife Catherine -- was vetted by others.
"It's not up to us to make that decision (to air). We just record it and then it goes to the other departments to work out," a sobbing Greig told Australia's Nine Network.
Christian added: "There's a process in place for prank calls or anything that makes it to air, and you know, that's out of our hands."
Greig and Christian have borne the brunt of global outrage following the apparent suicide of nurse Jacintha Saldanha, who fielded their hoax call.
The Indian-born mother-of-two put the call through to a colleague who divulged details of Kate's recovery from severe morning sickness.
Saldanha's "devastated" husband and teenage children made an emotional public appearance for the first time Monday outside Britain's Houses of Parliament, speaking through lawmaker Keith Vaz, whose family is also from India.
"This is a close family. They are devastated by what has happened. They miss her every moment of every day," said Vaz, alongside Benedict Barboza and the couple's children aged 14 and 16.
"They just want me to say that they are extremely grateful to the public here in the United Kingdom and throughout the world who have sent them messages of condolences and support following the death of Jacintha, a loving mother and a loving wife."
The family later visited the King Edward VII Hospital, which is launching a memorial fund to support them.
Following Greig and Christian's interviews, media pressure grew on Tuesday for the network to explain how the segment made it to air, with the Sydney Daily Telegraph claiming senior management were "dodging responsibility".
In an online report, the ABC's Europe correspondent added: "Some of the British media is asking the question, well, we still don't know who ultimately made that decision."
Rhys Holleran, chief executive of Southern Cross Austereo, which owns 2Day FM, has said the station called the hospital five times to discuss what it had recorded before going to air.
Under Australian regulations, the permission of anyone on the receiving end of a radio prank must be sought before the call can be broadcast.
But the hospital denied on Monday that anyone within its senior management or media unit was contacted.
Holleran insisted the appropriate checks were conducted before the pre-recorded item was broadcast, and defended the presenters in an interview late Monday with Australia's Ten Network.
Asked if anyone in authority above the hosts was at the station when the call was made last week, he said: "I think that it is important that these two individuals did not recklessly just decide to put something to air.
"They went through a process," he added, without going into details.
The stunt was vetted by lawyers before being aired, but no one else involved in the decision has been named.
The case has triggered demands for tougher regulation of the electronic media although Australia's press regulator, the Australian Communications and Media Authority, has not commented on whether the station broke any rules.
The government says the ACMA is considering whether to initiate an inquiry beyond its usual process of giving broadcasters 60 days to respond to complaints.