Final answer:
The U.S. modified its initial position stated in the Teller Amendment that it would not annex Cuba through the Platt Amendment, which allowed for U.S. intervention and control over certain aspects of Cuban affairs, including the establishment of Guantanamo Bay. While Cuba remained independent on paper, the U.S. heavily influenced their governance and foreign policy decisions. Aside from Cuba, the U.S. also maintained control over other territories such as Puerto Rico, Guam, and the Philippines after the Spanish-American War.
Step-by-step explanation:
The question revolves around whether the U.S. honored the Teller Amendment and what countries they did not leave post-conflict. The Teller Amendment was initially part of the declaration of war and forbade the United States from annexing Cuba.
However, it was modified by the subsequent Platt Amendment, which gave the U.S. significant control over Cuba's foreign policy and the establishment of the Guantanamo Bay military base. While Cuba did not become a U.S. territory and technically remained independent, the Platt Amendment allowed U.S. intervention in Cuban affairs, effectively placing Cuba under U.S. influence.
In practice, the United States did not fully honor the initial promise of the Teller Amendment, as demonstrated by the Platt Amendment's ratification. The Platt Amendment led to U.S. control over aspects of Cuban sovereignty, such as the right to intervene in Cuba's affairs. Despite the later revision of these agreements under Franklin D. Roosevelt's Good Neighbor Policy, the United States maintained its lease on Guantanamo Naval Station.
Regarding other territories acquired post-Spanish-American War, the U.S. did not annex Cuba but maintained control or influence over other territories such as Puerto Rico, Guam, Samoa, and the Philippines, with different levels of administration and governance depending on the territory. It is in these nuanced actions and amendments that America's stance on non-annexation is best understood.