I am not convinced about this theory. Here is why:
Firstly, papaya has the papain enzyme which is supposed to help with heartburn, vomitting and nausea that most women go through during pregnancy (atleast I did). I had so many of my colleagues who bought papaya supplements from GNC and took them every day to eliminate nausea and no one went into early labor. Atleast 5-6 of us were pregnant at the same time and we did what we could to support one another and share information and the papaya supplement was popular and it worked.
I also was in Hawaii when I was 4 months pregnant and ate papaya every single day (it was my favorite at the breakfast buffet and I was there for 15 days).
I boarded a catamaran to see the Napali coastline and the waters were choppy and the ride was bumpy. I think that would have induced my labor for sure but not the papaya