Final answer:
The country described, which gained its technical independence after the Spanish-American War but was subjected to U.S. intervention rights, is Cuba.
Step-by-step explanation:
The Latin American country referenced in the description is Cuba. Following the United States' victory in the Spanish-American War, Cuba was technically granted its independence; however, through the Platt Amendment, the U.S. was guaranteed the right to intervene to preserve order within the country.
This interventionist policy and Cuba's strategic importance to the U.S. meant that Cuba's independence was influenced by American interests for several decades after.