@Great Argus Yes, it would just look aesthetically beautiful in a photograph. I mean, I sure wouldn't want to have that bill lugged around on my face, I'm just saying in the photographs case its beautiful to look at.
@Terry Thomas No it's not, @Great Argus is right, it's the lower mandible of the beak. The bird probably bends his head to the side to pick up things, I don't know, didn't see him eat, he was pretty much always perched in the same tree.
@Rayane This can happen in the wild with Sword-bill hummingbirds, as they are not able to groom themselves properly because of their long pointed bill.