Zoomer, how could you, in good concience, send anyone to that hell-hole of a thread? But it was good reading...
My opinion based on fact:
The carrier, while being an M16 part, is not illegal in your AR15. It cannot make the gun function in FA, like an Auto-Sear, and it is not even part of the fire control group.
The reference to Bushmaster in that other thread was kind of amusing, since Bushmaster is fast to point out that they will sell you the RIGHT parts ASAP.
Bushmaster is in the business of sales. I have seen [private] letters from ATF on this topic and they strongly RECOMMEND that you don't possess M16 parts. That does not make it law, that merely is them letting you know that the presence of such parts can lead you down a bad path though ignorance or appearance.
This advice is usually given to those who already posses an MG and want to know the legaities of mixing & matching parts: uppers, lowers, etc.
The ONLY registered part is the sear, and they don't make any new ones for civilian use, so you better find one WITH papers.