I remember their website saying it. What they eventually did was break parts off the album and release them as connected singles. The art on these non-overlapping fragments plainly shows that they're all part of The King of Limbs. Indeed, they're from the same sessions. The band's recording technique was also intentionally out of order. Staccato. TKOL is one of their least appreciated albums because the weirdness lost even Radiohead fans, haha.
The author of a Stereogum article diving into this ("In Defense Of The King of Limbs") says he's made an uber-playlist of all the associated songs. A reintegrated album that works fantastically, but he doesn't give the ordering. Then someone in the comments offers one up. So a while back I made Ass-Kicked89's list a Spotify playlist. It's pretty good—yeah, yeah to say the least! My guess is that Radiohead wanted to encourage us to make our own playlists... a jigsaw puzzle album.
It would be seriously remiss to talk about The King of Limbs without sharing that many consider the filmed live performance (The King of Limbs: Live from the Basement) better than the original, "better" as in "so much better that these fans see it as the album itself." Definitely check that out, but I say give the complete playlist a try as well! Personally, I love it.
