Is it parody if the point is not to make fun of the original?

Little, Brown is publishing “Goodnight Bush,” an unauthorized parody of the 1947 children’s bedtime classic “Goodnight Moon,” written by Margaret Wise Brown and illustrated by Clement Hurd: The cover of “Goodnight Bush” looks almost exactly like “Goodnight Moon — green and orange, with an image of a window and fireplace — and uses a similar rhyme scheme. But there the thematic similarities end.

The authors, Erich Origen and Gan Golan, set their story in “a situation room.” There is no bunny snuggling into bed, but rather George W. Bush, grinning and wearing a “Mission Accomplished” flight suit. Instead of three little bears sitting on chairs, there are “war profiteers giving three cheers.”
Subsequent pages tell of “A grand old party to war in a rush/And a quiet Dick Cheney whispering hush.” The vice president is illustrated seated in a rocking chair — with a shotgun in his lap and bunny slippers on his feet. . . .

The publisher of “Goodnight Bush” is counting on the fair use doctrine, which allows limited amounts of copyrighted material to be used without permission. “Parody as fair use is a developing area of the law,” said Pamela Golinski, an entertainment lawyer in New York, “and as a result, whether a given parody merits the shield of the fair use doctrine is a complex question.”

Little, Brown may have some difficulty in sustaining its fair use defense in light Dr. Seuss Enterprises, L.P. v. Penguin Books USA, Inc., 109 F.3d 1394 (9th Cir. 1997), in which the U.S. Court of Appeals for the Ninth Circuit held that the re-telling of the facts of the O.J. Simpson murder trial in the style and rhythms of Dr. Seuss's The Cat in the Hat was not fair use. The court concluded the book was a satire, not a parody, because the book did not poke fun at or ridicule Dr. Seuss. Instead, it merely used the Dr. Seuss characters and style to tell the story of the murder.

Readers of this blog will not be surprised to know the parody/satire distinction seems a tenuous one. Every parody makes a point independent of its ridicule of the original, and every satire requires recognition of the original to accomplish it's artistic intent. Do the copyright holders to The Cat in the Hat own its metrical scheme?