This guy seems to be saying (at 2 min 10 sec) that if the rifling twist is not fast enoug the bullet will be ok for very short distances but will start key holing soon after. http://www.atactv.com/video/571/Product-Review-Tula-Krink
I am on a crap connection right now and the video won't load for me. Bullet stability doesn't work like that, it is at its lowest stability level as it leaves the muzzle. This is because the destabilizing force is proportional to forward velocity while the stabilizing force is proportional to the rotational velocity of the bullet. Forward velocity decays much faster than rotational velocity, so the bullet gets more and more stable as it flies and loses velocity.
The only thing I can think of is he is referring to marginally stable bullets that may print clean holes up close (less than 25yds, say), then start tumbling soon after that. This is a case of an unstable projectile, it just takes a short distance before the instability can actually cause it to start tumbling.
Mark