I've looked into this issue a while back, and there really is no definitive answer as to the legality of doing it. Please note that the CFC site states:
Prohibited firearms include:
* rifles and shotguns that have been altered by sawing or other means so that their barrel length is less than 457 mm (about 18 inches) or their overall length is less than 660 mm (about 26 inches);
Which technically means(according to the CFC site) if you cut(saw) down an AR(rifle) barrel and that barrel ends up less that 457mm then you have a prohibited gun. Installing a <457mm factory AR barrel is perfectly legal.
FWIW there are some smaller gunsmith shops that do this work, and the alteration was verified by the CFC. I remember asking Prairie Gun Works about chopping an AR barrel and they have told me that besides the fact that it will ruin the chrome-lining, it is illegal to chop an AR barrel to less than 457mm. YMMV.