I think you're (understandably) misreading a poorly designed insert. I don't think it's meant to imply that "Stone's Egg" is Edge's only contribution (though it very well may be; it's the only one where you can clearly identify Edge stylings). I think the artist list is simply a right-hand column that, to make things aesthetically interesting, has been weaved through the left-hand column of songs, but that there is no real correspondence between where a song is listed and any artist listed above or below it. For instance, Edge is listed below "Stone's Egg"; so if that placement indicates that's the single track he's involved with, what do we make of Michael Brook, who's listed above all songs? Or Kevin Shields and David Silvian? Are they both involved with the track "Her 200 Bones" or are there just more artists to list than tracks? I think it likely that all of these artists contribute throughout these tracks in a very random fashion, so we'll likely never have definitive proof of the extent of Edge's contribution unless he or Russell Mills is interviewed about it...
By the way, assuming you are talking about the LIVE 8 performance of "Sgt. Pepper's" with Paul McCartney, if you buy the DVD and have a DVD-ROM, you can make a very nice, high-quality audio rip like I did...