I think that Dumbledore's "Remember my last" is a reference to a previous letter he sent to the Dursleys explaining why they must keep Harry. Harry has to have a place to call home so Voldemort cannot harm him. But I do think that Petunia knows a lot more about the magical world that she cares to admit. She knew what dementors are, and she's always saying that her parents were so proud to have a witch in the family. There has to be more to her story than what we know.
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