All American units in Vietnam, from the division level down to the battalion level and down to the squad level, were responsible for knowing and acting in accord with rules of engagement, which usually came down from the headquarters of the U. S. Army in Vietnam (USARV) or, depending upon the unit involved, the Military Assistance Command, Vietnam (MAC-V).
The Rules of Engagement changed slightly from the beginning of the U. S. involvement to the end--that is, the ROE in the mid-1960's were more limiting than they were in 1969-1969, for example. After 1969, when the U. S. begin a steady draw-down of U. S. combat and support troops, the ROE became more restrictive again, this time to insure less U. S. involvement in the actual fighting than in earlier years.
In many cases, the ROE didn't actually change, but the terms that the military used for certain operations changed to reflect political correctness, and therefore the general public may have believed the ROE had become more restrictive. For example, in 1965-1967, Army infantry routinely engaged in "search and destroy" missions in which they would burn down a Vietnamese village suspected of either housing or supporting Viet Cong (Vietnamese communist guerrillas) or North Vietnamese troops. This phrase was banned sometime between 1967 and 1968, but the missions carried out had the same effect, but they were often called "pacification" operations--a meaningless difference, but it sounded almost humane.
Unfortunately, given the nature of the war in Vietnam, the ROE became "guidelines" that were often completely ignored at the company and platoon levels, not all the time, but often enough for people at higher levels to notice. Some divisions were more likely to try to adhere strictly to the ROE than others were, but to generalize about the extent to which ROE was observed is essentially useless.
Battalion commanders had a greater degree of operational freedom than their superiors, although they did not always utilize that freedom. It did depend on what kind of force they were leading and what operations they were charged with carrying out.
One of the more well known and highly decorated battalion commanders in Vietnam, Colonel David Hackworth, is considered by many military historians to have been exceptionally good at battalion level operations. He served in the 101st Airborne Division during that war, developed and wrote The Vietnam Primer on counterinsurgency operations and adopted guerrilla warfare tactics that matched the style of fighting used by the Vietcong (Tiger Force).
As with most good battalion commanders, he understood how important it was to follow orders such as the ROE, while at the same time knowing how far he could bend those rules to make his units effective in combat while still making his superiors happy. In this sense, I think that was a typical experience for these commanders, who were charged with effectively carrying out missions despite their limitations. Those who could find a way to fight even with one hand tied tended to get promoted.