That thing he did at the start of Medicate in Octavarium is my fav, but it's not really a solo, right?
Where's Scarred? From 0:05-0:26. He plays the whole thing there, including the chords.
From my point of view, those two are not solos.. They're chord progressions, riffs or phrasings that kicks off a section, like these parts: Learning to Live (right before first verse), Caught in a Web (after instrumental part), New Millenium (beginning), Blind Faith (beginning) and Breaking All Illusions (before first verse), etc...
All these parts (along with the already mentioned Scarred and Medicate) usually have the guitar and the keyboard doing not only a certain variation of notes, but also the main melody in that part (or even in the whole song).. In the quoted examples, that role belongs to the bass; that's the only difference...
And regarding the fact that playing the whole thing is doing a solo, he has the beginning of Panic Attack and A Rite of Passage's, and two times throughout Enigma Machine, where he's the only one playing and where he's obviously not doing any solo..