The ammunition conservation angle is supported by primary sources, but not as a result of Vietnam "spray and pray". The M16A2 was originally a USMC program, and the USMC is an expeditionary force, with all the attendant logistical constraints. At the time that the burst requirement for the M16A2 was set, the USMC had recently adopted the M249 Squad Automatic Weapon. Previously, the designated automatic rifleman role at the squad level was filled by an M16A1 with a bipod; the US services did not transition to a belt-fed at the squad level until the adoption of the M249. The USMC foresaw much higher ammunition expenditures with the M249, which could potentially pose a problem for the logistics constraints of a shipborne expeditionary force. Within the squad and platoon, it was further viewed that having everyone possibly firing on full-auto would deplete ammunition that could be better used by the M249 gunner, as his weapon would be more effective in that role than aimed automatic rifle fire. The decision was thus made to strike the automatic fire capability from the M16 altogether. The program manager for the M16A2, Col. David Lutz, was given the choice of a safe/semi rifle, or a safe/semi/burst rifle; he chose the burst, as having a semi-only rifle in the 1980s was deemed too limiting.

Most of the information here can be found in Stevens and Ezell's The Black Rifle: M16 Retrospective, as well as in an interview with program manager Col. Lutz and in various unclassified DoD reports. There's no single report that covers all of it, but if you go through the 1970 Army Small Arms Requirement Study, the 1964-1966 Small Arms Weapons Systems Study, and the 1961 Rifle Squad and Platoon Evaluation Program report you'll start to get a handle on the technological, tactical, and institutional factors at play.