Friends in her native India have described her as a devout Catholic who was generous, dedicated and caring toward her patients.
The hospital released a letter late Friday sent by chief executive John Lofthouse to lawmaker Keith Vaz, who has been supporting the Saldanha family.
In it, Lofthouse spells out the guidelines given to staff for dealing with calls when a "high-profile patient" is being cared for -- and insists that Saldanha was given full support by the hospital.
"Part of our procedure is to take the name and number of the individual and call them back. This is in order to verify that the call is genuine. We also empower our staff to use their judgement," he wrote. "On this particular occasion, Jacintha believed that the call was genuine, and she felt it appropriate to put the call through. We stand by her judgement."
After the hoax call Saldanha was reassured a number of times by senior managers that she was not being blamed for anything, he said, "and there were no disciplinary issues involved, because she had been the victim of a cruel trick."
Saldanha was also offered further support, including time off, the chance to return to her family home in Bristol or counseling, but declined to take it, he said.
"Jacintha said that she would prefer to continue working. Neither ourselves, her friends or family noticed anything to give cause for concern."
Lofthouse said he had been in touch with Saldanha's husband and that the family had now accepted the hospital's offer of support. The hospital will do all it can for the family "at this desperately sad time," he added.
The media network that owns the 2Day FM, Southern Cross Austereo, has also said it will donate a minimum of 500,000 Australian dollars (US$524,000) to a fund for the nurse's family.
Responding to reports of death threats against the DJs involved, Michael Christian and Mel Greig, Southern Cross Austereo said Friday that the safety of its employees was "an absolute priority."
"We have sensible measures in place, as we always do, to ensure our people are safe. This is now a matter for the police and we trust they will investigate any specific threats that emerge," a spokesman said.
The DJs made a heartfelt apology in TV interviews in Australia this week, saying they had meant no harm.