What's interesting, from a jazzer's perspective, is that a melody and an improvisation on that melody can flow through chords that don't appear to be the "right" chords, or even substitutes for those chords.

Basically, you can put whatever chords you want to any tune in any key. Whether they sound right, wrong or indifferent - or anywhere near to the composer's intentions is all in the ear of the arranger. The reality being, of course, that to go way off track produces dischords which might be completely incomprehensible.

An interesting example of chord complexity/simplicity arises when you put chords behind melodies such as Christmas carols. Most carols will function with a very simple chord structure - perhaps just two or three chords - but will also support incredibly complex and architecturally interesting harmonies (say in a choral setting). You can find similar examples of alternative/substituted chording in tunes in a range of music from jazz to folk tunes. The correctness or otherwise lies within the taste of the player and the listener.