The Supreme Court case of State of Oklahoma v. State of Texas, with the United States as an intervener in 1923, was a dispute over the ownership and control of oil-rich lands along the Red River boundary between Oklahoma and Texas. The controversy arose due to differing interpretations regarding where exactly the border lay: whether it was on the south bank or along the river's gradient line (the midpoint between normal high and low water marks). The U.S., which had granted land patents to both states based on their respective claims, intervened for clarity. In its decision, following extensive historical research into treaties and past decisions related to such boundaries, including those involving riparian rights (rights relating to bodies of water), navigability issues etc., The Supreme Court ruled that under international law principles applicable at time when these territories became part of U.S., boundary is along south bank - not gradient line - thus favoring Texas' claim.

In the dissenting opinion for the case of State of Oklahoma v. State of Texas, Justice McReynolds disagreed with the majority's decision to grant ownership rights over a disputed portion of land along the Red River boundary to Texas. He argued that this ruling was inconsistent with previous decisions and treaties regarding state boundaries. According to him, these earlier agreements clearly established that when a river is used as a boundary between states or nations, changes in its course do not affect existing borders unless they occur suddenly due to natural phenomena such as floods or earthquakes (avulsion), rather than gradual shifts (accretion). In his view, since there was no evidence suggesting an avulsive event had occurred on this part of the Red River border between Oklahoma and Texas during relevant timescales, it should be presumed that any alterations were due to slow accretionary processes which would not alter jurisdictional lines under international law principles adopted by U.S courts. Therefore he concluded that Oklahoma should retain sovereignty over lands northward from south bank’s edge at time when Indian Territory became part thereof.