Kind of obvious, but I'll throw it out there anyway: Who else thinks Juliet's sister, Rachel, never had a cancer relapse?
Think about it. Ben says Rachel's cancer is back, and that she will die before the baby is born. One of Juliet's reasons to leave the island (i.e. to be with Rachel when the baby is born) is moot, and the other reason (to be with Rachel when she dies) is eliminated with Ben's "promise" to cure her of cancer and save her life if Juliet agrees to stay. So, Juliet stays.
Then, when Juliet accuses Ben of lying about Rachel because he now apparently has cancer, and demands to leave, he shows "proof" that he kept is promise: Rachel is cancer-free with a healthy baby.
All of the above could easily, and more simply, play out if Rachel's cancer never returned in the first place, and those medical records Ben showed to Rachel of the cancer's returning were simply fakes.
Occam's Razor, doing its thing again.
Thoughts?
Later,
Atavar