The De Arnaud v. United States case in 1893 revolved around a dispute over land ownership in California, which was originally granted by the Mexican government before the territory became part of the U.S. The plaintiff, De Arnaud, claimed that he had purchased this land from its original grantee and therefore held rightful title to it under the Treaty of Guadalupe Hidalgo. However, his claim was rejected by both lower courts and eventually reached the Supreme Court. The Supreme Court upheld these previous rulings against De Arnaud's claim on two main grounds: firstly because there were discrepancies between his description of the property and official surveys; secondly because he failed to provide sufficient evidence proving that he had fulfilled all conditions required for validation of such grants under Mexican law (such as occupying or cultivating said lands). Therefore, despite acknowledging that some rights established prior to American acquisition should be respected according to international law principles embodied within treaties like Guadalupe Hidalgo - they ultimately ruled against him due lack of proof regarding compliance with those very same laws.

In the dissenting opinion for De Arnaud v. United States, Justice Brewer argued that the court majority had erred in its interpretation of the law and constitutionality surrounding citizenship rights. He contended that Mr. De Arnaud's naturalization as a U.S citizen was valid despite his subsequent return to France, where he lived until his death. According to Justice Brewer, once an individual has been granted U.S citizenship through proper legal channels and procedures, it cannot be revoked or nullified by any other country’s laws or actions unless they willingly renounce their American nationality themselves or commit acts leading to expatriation under U.S law. Therefore, he believed that Mr. De Arnaud remained a US citizen at his death regardless of living abroad and should have been treated as such regarding inheritance issues involved in this case.