Stockton and Kearny went on to recover Los Angeles and force the capitulation of Alta California with the "Treaty of Cahuenga" on January 13, 1847. As a result of the Mexican–American War of 1846–48, the territory of Alta California, including San Diego, was ceded to the United States by Mexico, under the terms of the Treaty of Guadalupe Hidalgo in 1848. The Mexican negotiators of that treaty tried to retain San Diego as part of Mexico, but the Americans insisted that San Diego was "for every commercial purpose of nearly equal importance to us with that of San Francisco," and the Mexican-American border was eventually established to be one league south of the southernmost point of San Diego Bay, so as to include the entire bay within the United States.
Why was the border between Mexico and the United States established one league south of San Diego Bay's most northern tip?