Final answer:
The statement is false; British Invasion bands were heavily influenced by American rock and roll and African American musical traditions. This influence can be heard in their music and the American songs they covered.
Step-by-step explanation:
The statement that very little American influence can be heard in the British Invasion bands in the 1960s is False. Groups like Cream and The Rolling Stones were significantly influenced by American rock and roll, rhythm and blues, and other African American musical traditions. This influence is evident in their music styles and the covers of American songs they often performed. The British Invasion actually represented a re-interpretation of the American music that had inspired these bands, such as the works of Chuck Berry, Elvis Presley, and Muddy Waters, among others. British bands brought this influence back across the Atlantic, creating a unique fusion that proved to be wildly popular on both sides of the ocean.