In the 1905 case of Alexander v. Crollott, the U.S Supreme Court ruled in favor of Alexander, who was appealing a decision made by Justice Crollott. The dispute arose over land located within an Indian reservation that had been allotted to individual members under federal law but was later sold to non-Indians. According to Oklahoma territory laws at that time, such lands were exempt from taxation until they were sold and transferred out of Indian ownership. However, when Alexander purchased the land from its original allottee (an Osage tribe member), he found himself facing tax claims on it for previous years when it should have been tax-exempt. Alexander argued these taxes were illegal since they violated federal law which protected such lands from state or territorial taxation while still owned by Indians or their heirs. The lower courts disagreed with him and upheld the validity of those taxes. Upon appeal to the Supreme Court however, his argument prevailed as justices agreed with his interpretation of federal law regarding this matter - thus ruling against Justice Crollott's earlier decision.

The dissenting opinion in the case of Alexander v. Crollott, Justice of the Peace, argued that there was no violation of due process rights as claimed by Alexander. The justice opined that while it is true that a person cannot be deprived of life, liberty or property without due process of law, this does not mean they are entitled to any particular form or method for protection against state action. Instead, what matters is whether there has been an opportunity given for hearing and defense before judgment is rendered. In this case, according to the dissenting view, such an opportunity had indeed been provided and therefore no constitutional right had been violated.