I found those claims odd because the M16s have been serialized since the very beginning.
We inventoried M16s 10,000 at a time. It was a full production, requiring teams to arm up, open up the cases, sometimes clean them, and then place them individually on the table where two MSgts would confirm each serial number (viewed either directly or through the window in the vacuum sealed foil bags), and they'd sign the weapons card. No one was going to put their signature on a card for a suspicious weapon. The M16s were then often vacuum sealed in bags, if they weren't already, and then eventually shipped out.
The only part of the M16 that is serialized is the lower receiver. The barrel assembly (which was damaged in this video) can be interchanged with an undamaged barrel assembly. The lower receiver is the only part that matters when taking accountability of a particular rifle.