If there was an original issue XM16E1 or early model M16A1 in service in 1971; that suggests additional problems besides this well documented failure.
An improved XM16E1 was re-designated M16A1 in 1967, so there should not have been a XM16E1 in combat in 1971. The XM16E1 had the charging handle under the carry handle and had no forward assist. The first designated M16A1 had the charging handle on the rear of the receiver, no forward assist and the chamber was not chromed. The early powder manufacturer could not provide the demand needed, so it was replaced early with a new, dirtier powder. In 1970, a newer WC 844 powder was introduced to reduce fouling. Some troops may have been issued this ammunition with the dirty 2nd gen powder in 1971. The early M16A1 did not have the improvement of a chrome chamber and barrel, so this combination, as well as documented inadequate care and cleaning, resulted in these failures. The combination of a chromed chamber and barrel, new powder, and issuance of instructions for care and cleaning, greatly reduced chamber sticking and fowling. The later M16A1 had the forward assist and chromed chamber/barrel.
Think about the described failure. With a stuck casing, the rifle attempted to extract to the point of separating the case head from the body (a problem sometimes in bolt guns), breaking the extractor, and then still picked up another round and attempted to chamber. Some say this suggests a robust internal operating system and not a design problem, but rather a combination of secondary issues that have since been remedied. Today, there is the choice of a gas piston impingement system, or the original direct gas impingement (DGI) system (SR556 v. AR556). Some choose the AR556 (DGI) as parts are more plentiful and cheaper; some find the system simpler to work on and a little more accurate. The piston system runs cooler and cleaner but may be somewhat less accurate (not an issue with many). If one buys the cheaper DGI rifle, he can purchase a piston driven upper and install it on the DGI lower. The modern day systems and ammunition work and are depended on worldwide.
Our choice(s) are our choices. Depending on circumstance(s), one can have too much gun, as well as too little, both can have unintended circumstances and results. It is great to live in a time and country where we have these choices in armaments, and individual responsibility for their use. John M. Browning rightfully has a place in firearms development history worldwide, as does Eugene M. Stoner.
Regards and Semper fi
USMC 1964-68 (3rd MarDiv 1966-67)