Was Cuba truly independent after the Spanish-American War?

yes

Explanation:

However, the Spanish–American War resulted in a Spanish withdrawal from the island in 1898, and following three-and-a-half years of subsequent US military rule, Cuba gained formal independence in 1902.

then its a law the end

no every country is held to the same degree as others just some member countries such as the usa and germany are more economically sound so the need to show there support to all others