No, of course not. People misattribute causes all the time. She had already attempted to kill herself twice, but we can be certain that the prank call wasn't involved in those. I estimate that the responsibility for the successful suicide can be attributed nearly 100% to whatever it was that caused the other attempts, and less than 2% to the prank call, humiliation at work, national visibility, etc, that resulted. The prior suicide attempts have so much explanatory power that almost nothing is left over for the prank call, no matter what one of her suicide notes said. She left another suicide note (same suicide, separate note) complaining about the management at her hospital, with whom she had had ongoing difficulties. Should we conclude that you shouldn't adopt policies that some employees don't like, because someone might kill themselves?
Rough impression of where I picked numbers like "nearly 100%" and "less than 2%": two questions. First, of the people who become nationally notable in some minor but arguably humiliating way (she wasn't even the staffer primarily targeted by the prank call; it's not clear to me whether anyone outside the hospital would have known she was involved), how many attempt to kill themselves? Second, of the people who attempt suicide twice, how many attempt it a third time?
Just to be clear, I don't endorse prank calling at all; I'm glad it's a dying "art". But the death of Jacintha Saldanha isn't evidence for anything more than "people who are determined to mess up their own lives, can".