In canon, Hermione says it means exactly as Lupin thought, and Harry believes her (and J.K. Rowling intended it like that). As some of J.K. Rowling’s quotes (no sources at the moment) about canon seem to imply that she does not see her interpretation of the books is just as valid as anybody else’s, the idea that a descendant of Harry’s could go to the graveyard of the Peverells, announce plans to defeat Death, and get HJPEV’s results is canon-compliant.
In canon, Hermione says it means exactly as Lupin thought, and Harry believes her (and J.K. Rowling intended it like that). As some of J.K. Rowling’s quotes (no sources at the moment) about canon seem to imply that she does not see her interpretation of the books is just as valid as anybody else’s, the idea that a descendant of Harry’s could go to the graveyard of the Peverells, announce plans to defeat Death, and get HJPEV’s results is canon-compliant.