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In the Page Table section of the Paging wiki:

D, or the Dirty flag, if set, indicates that page has been written to. This flag is not updated by the CPU, and once set will not unset itself.

That sounds wrong or at least confusing. Am I missing something?

It is not reset by the CPU. It will be set by the CPU, but once set, it will never be reset by it. You have to reset that bit when you need to. Same goes for the access bit, by the way.