No, there are some other stories out suggesting that Kennedy is royally ticked off at Roberts, and that he’s talking about it on background to some media acquaintances of his.
To my mind, it seems obvious that Justice Kennedy is one of the sources for this story. Go back and read Crawford's original print report. Who comes off looking best in her account? That Kennedy is something of an egomaniac is consistent with his being involved with the story being "leaked" the way it has.
Also, as best I can recall, the Crawford story contains no representation to the effect that she attempted to contact the Chief Justice's office for comment (I know that Roberts left for Malta shortly after the end of the term, but he has an administrative staff, of course.) That the story makes no such representation indicates that no attempt was made. This, in turn, suggests to me that Crawford (and her editor(s)) have what they consider to be rock solid "sources" -- i.e., another Justice.