If you consider the photo taken by Nick Ut of the Vietnamese girl Kim Phuc running after the napalm attack , that photo is not technically brilliant, but the subject matter and what it coveys is so powerfull that it can be classed as a great shot.
It's able to capture that moment, so in that sense I would say the subject is the most important aspect of a photo.
Phan Thị Kim Phúc - Wikipedia, the free encyclopedia