Probably not true? Though Wikipedia isn’t an authoritative source obviously:

There is a popular belief that the name has its origins in World War II when American G.I.s in Italy diluted espresso with hot water to approximate the coffee to which they were accustomed. However, the Oxford English Dictionary cites the term as a borrowing from Central American Spanish café americano, a derisive term for mild coffee, dating back to the middle of the 1950s. Its first use in English appeared in the Jamaican newspaper The Sunday Gleaner in 1964. The term caffè americano entered Italian later than the English or Spanish uses, suggesting the term originates outside of Italy.