I know it sounds counterintuitive, but the 5.56 DOES stabilize in flight, about 50 feet out, IIRC. It has to do with the geometry of the bullet, long and thin with a very small radius relative to length, and the fact that no bullet ever centers perfectly with the center of the bullet lined up with the center axis of the bore. That's why they need stabilization in the first place. The difference with the 5.56 as opposed to others is like the difference between a spinning football and a long spinning steel rod: the rod wobbles for a bit, then damps down as the rotational forces take hold.
Anyway, that is what the guys from our firearms unit, who want to eliminate subguns and shotguns in favor of M4's for everything, told me. Actual shootings seem to bear this out: within 50 feet the bullets stay in what they hit, further out they can drill a steel plate.
I'd be happy to entertain alternate explanations, though, for entertainment value if nothing else.