Westmoreland’s proposal to explain his recommended action in Cambodia as “hot pursuit by fire” was an attempt to solve the crux of the Cambodian dilemma as it appeared to American policymakers throughout the Vietnam War: how to warp the red line that a sovereign border represented without ignoring it entirely. As the economist Thomas Schelling put it the previous year in “Arms and Influence” — something of a strategic playbook for key architects of the American war in Vietnam — the “purpose of invoking ‘hot pursuit’ is not merely to find an excuse for it but to identify a limitation in intent, to let the enemy appreciate that his is not an abandonment altogether of some previous restriction but an allowable departure under the rules of the game.”

A number of Johnson’s advisers were skeptical of this logic. They thought that rather than signaling limited intent, an appeal to a right of hot pursuit would more likely be seen as feeble cover for a significant change in policy.. Averell Harriman, ambassador at large and one of Johnson’s foreign policy “wise men,” tried to convince the president that “the world at large (and a substantial section of the American public) has not yet been presented with convincing evidence that expanding the war into ‘a tiny, helpless country’ is justified.”

In any case, despite the assumption of Westmoreland and Schelling, hot pursuit was not widely accepted as an allowable departure under the rules of the game. It had no standing in international law (except within the law of the sea, which allows for the hot pursuit of vessels into international waters), and since at least March 1965 the State Department Office of the Legal Adviser had rejected it as an appropriate justification for crossing the Cambodian border. The lawyers insisted instead that any legal argument for border crossing would need to rest on the right of self-defense guaranteed by Article 51 of the United Nations Charter.

The legal basis for the American bombing of North Vietnam rested on the collective self-defense of South Vietnam. But the logic of self-defense regarding Cambodia was different: Whereas the government of North Vietnam could conceivably be linked to military attacks against the government of South Vietnam, the government of Cambodia could not. Absent a sudden threat that left no time for deliberation, Washington would therefore need to show Cambodian “connivance” in the use of its territory before launching any attack on Cambodia. The Cambodian head of state, Prince Norodom Sihanouk, often appeared to be more friendly to the communists than to the Americans, but substantial evidence of connivance did not surface.

Particular military units engaged with the enemy had authority to fire over or cross the border if necessary to defend themselves. (On Dec. 5, Rusk suggested that this authority might still allow Westmoreland some freedom of action: “I would have thought that Westy would have drug his shirttail along the Cambodian border and drawn enemy fire. Then the rules would permit him to shoot back across the border when fired upon.”) But beyond this, and the limited covert reconnaissance operations code-named Daniel Boone, no further authority was granted. On Dec. 18, Johnson effectively ended the debate over Westmoreland’s request. The United States would instead focus on trying to convince the Cambodian government to be more assertive in the defense of Cambodian neutrality, or to let others act to preserve that neutrality.

Johnson’s successor in the White House made a different decision. President Richard Nixon approved B-52 strikes on suspected enemy locations in Cambodia from March 1969, and at the end of April 1970 he sent American ground forces across the frontier to find and destroy enemy sanctuaries. The catalyst for the 1970 Cambodian incursion (or invasion) was the overthrow of Sihanouk and the establishment of a more pro-American government in Phnom Penh. But even this government sought to preserve Cambodia’s neutrality, meaning it could not formally invite American troops into the country.