I own an early Eighties Charvel Strat that I absolutely love. Unfortunately, certain chords, specifically open D variations, don’t ring in tune, even when I use my tuner. It drives me nuts! My guitar teacher checked the intonation and said it was right on. What could be wrong?
More than likely, worn frets are your culprit. For a guitar to intonate properly, all of its frets should be of equal height. Over time, however, the frets in the most heavily played areas of the fretboard wear down, while frets that receive lighter use remain relatively unchanged. As a result, not all the strings intonate correctly, causing some of the sounded notes to be slightly out of tune.
What really has you and your teacher confused is why the guitar is tuning and intoning correctly. This is happening because, like everyone, you’re using the 12th fret harmonic to tune and intonate your guitar, and I would guess that the frets in this area of guitar’s neck are even and level with one another. This gives you a false impression that your guitar is intonating properly. The problem more likely is occurring around the 2nd and 3rd frets, as this is typically the most heavily played area of nearly every guitarist’s fretboard.
Worn frets will be visible to the naked eye, so loosen the strings, pull them away from the fretboard and look for divots and flats spots. Most frets are tall enough that they can be filed down and evened out a few times in their lives. This will probably be the case with your Charvel, and it is certainly the most economical route for you to take. You could also consider a complete refret, but it’s probably not necessary.