The New York Times has not "admitted" any such story in any way, shape, or form, nor did they report anything regarding the two buddies as concluded since that sordid tale is quite literally very much unfolding everyday.
There has been much speculation and accusations that haven't been substantiated, but with the ongoing release of emails, photos, and a client list waiting to be freed from Pam Bondi's desk - all redacted, the complete story is far from told, nor will it ever be told completely.