This is a reference to the oracle in the sanctuary of Dodona, Epirus:
During classical antiquity, according to various accounts, priestesses and priests in the sacred grove interpreted the rustling of the oak (or beech) leaves to determine the correct actions to be taken. According to a new interpretation, the oracular sound originated from bronze objects hanging from oak branches and sounded with the wind blowing, similar to a wind chime.
However, we have no way of knowing if the piece of wood that fell from the stern and killed Jason was part of the keel (and thus had originated in Dodona).
Furthermore, mythologically it doesn't quite fit. Dodona was Zeus' sanctuary and Jason's death was an act of Hera (for Jason had betrayed Medea). These two were very rarely allied, and Hera had no reason to risk angering Zeus.