Yes, that's right: as Prim says, "the film evokes what the book evokes" -- or rather, both of them evoke something, point to something, that speaks to my heart (sometimes I might even say: that IS my heart).
So it's not like cover art on a book at all, because the cover is subordinate to the book, whereas in the LOTR case, both book and film are imperfect but precious reflections of Something Else.
(By the way, for me the Harry Potter movies are EXACTLY like cover art! Pretty pictures to illustrate the book.)