I guess I'm of a diferent mind on this discussion. I don't believe you can be one or the other. I am neither tuneocentric or chordocentric. You almost have to be equally aware of both as you determine how to play a song.
At a certain level of experience you feel the chord that is needed based upon how the melody travels as you sing.
If you are playing melody only and are at a certain level of experience the same thing happens. Either you sing aloud the melody you are playing and then add chords to round out the performce.
Just as The Guest stated when talking about Ian Anderson's rendition of the J.S. Bach Bouree from Jethro Tull's "Benefit" album. Get the melody and fill in with the chord.
I don't think it matters if you are sing a melody and then finding the chords, or playing the melody and filling in the chords. I think we as musicians does this unconciously at some levels and are unaware to what extent we rely upon the equal balance of melody and chord to complete a piece of music.