Suggestion: the person who memory charmed Rita Skeeter was Gilderoy Lockhart, who was the most famous master of Memory Charms ever mentioned in canon.

That might explain the first sentence of Albus Dumbledore's aftermath in Chapter 63: "It might have been only fifty-seven seconds before breakfast ended and he might have needed four twists of his Time-Turner, but in the end, Albus Dumbledore did make it."

Or perhaps not, since there would presumably be more than 4 hours between 2am (when Trelawny heard the prophecy) and the end of breakfast.