Not my genre at all but in general chords are really just harmony so whether they matter or not depends on what you are wanting to achieve. Some music (eg Indian classical) dispenses with harmony entirely while "conventional" melodies may well suggest certain chords and progressions.
In metal and some folk music, power chords (ie chords with only the 1st and 5th of the scale) are commonplace so "what sounds right" could include those or you could get way more complex. I have just been to a concert where I heard a song I knew intimately played against an almost entirely different backing. It sounded strange indeed but I decided I liked it. Here are the two versions (er... maybe a Folk Music alert is required!):
https://www.youtube.com/watch?v=zCnJdQ9izto
https://www.youtube.com/watch?time_c...&v=r0sm4jkaejY
(Some of the melody is changed too!)
In short I agree -it's what sounds right.