Marianne Faithfull sang it with her meaning, as stated in Wikipedia, but Shel Silverstein was not known for his happiest of endings.
The rest of the lyrics contain a deliberate and provocative contempt of women, in context of the time Silverstein may have been taking a pop at the new wave of feminists, like Erica Jong.
So I am sticking with she jumped. But I don't suppose there is a right or wrong answer.