They make that noise when they are bent a bit too, but then you get kind of a funky flight out of them as well. I know what you mean about the loose point noise. This was different, kinda hard to describe. The closest sound I can equate it to was when I used to work in a metal fabrication shop. When we'd put a large piece of 12 to 14 gauge sheet metal on the shear table, it sounded similar.
I think my son plucked the string enough to get the arrow to bang into the riser and the noise was the arrow trying to recover from that combined with paradox and the fletching fighting to straighten things out. The point was tight; I checked that when I picked his arrow up for him.
I wasn't hearing this from an arrow I shot. I was about 10 yards to the side of where he was shooting. I had him shoot the same arrow again and all I heard was a slight hiss from the feathers, so it wasn't an equipment problem. Still, I don't think you could get a similar sound from wood or carbon.