My naive approach is to consider intonation at the 12th fret. The instrument has proper intonation if the overtone at the 12th fret is the same frequency as the fretted note there. So a compensated nut lets you adjust the vibrating length of the string. The 12th fret can't move and you presumably cannot adjust the bridge anymore so the only thing left is the nut.
I think some of the confusion comes from overloading (software term for a fellow geek) the word "intonation". When you are talking about physically setting up a guitar it means one thing but when you are talking about playing music on the guitar and being "in tune" it means something else and needs the context of "well tempered" or Western Harmony or some other understanding of the compromises between theoretical physics and musically realities.
My experience has been that "intonation" means different things when I play(ed) tuba and when I play bass guitar and the things I do to get in tune, generally and the things I do to make a specific note sound right in a particular chord or context.
Jaime,
I would suggest that intonation for a fretted instrument refers to the accuracy of the pitch of a note, be it "open" or fretted. This definition easily lends itself to guitar design, construction, set up, retrofits, etc.
Temperament (Pythagorean, meantone, just, equal, etc.) refers to adjustments made over the centuries to address intonation discrepancies that were introduced as stringed instrument music moved away from single plucked notes and incorporated harmonies (e.g., chording, playing multiple notes at once, something we now take for granted on a guitar, was unthinkable at one time). There is so much to choose from today, in terms of tones, scales and octaves, and so much more accuracy is demanded from an instrument today than from those early predecessors of the guitar.
One of my favorite treatises on the topic was put together by (now retired) luthier Mike Doolin. It is still available on his web site:
Mike Doolin on Intonation
