When Fran was pregnant, the squadron flight surgeon recommended she stop flying herself in the third trimester because of the possibility of unexpectedly going into labor. They recommended against her flying even on the airlines in the last two months, and the OP's 32 weeks is well into that period. All I can say is I would not want my passenger in a light plane suddenly announcing, "Omigod, my water just broke," and from what I know about pregnancy (admittedly, purely as a spectator), that's a distinct possibility without warning at/after 32 weeks. So, it would not surprise me in the least if the OP's potential passenger's OB had given such advice.