Winston Churchill was the prime minister of Great Britain during World War II and took the office after Neville Chamberlain resigned in 1940. Churchill led Great Britain to victory and was a key figure in organizing the Allies to defeat the Axis Powers.
They trusted him because he was an ally.
Winston Churchill was a British politician and army officer. He was the Prime Minister of the UK during WWII, when he led Britain to victory along the Allied Powers. Americans would trust what he had to say about the Soviet Union because America was also apart of the Allied Powers and Britain was one of America's strongest allies.
He was the prime minister of England. England was one of the United States's closest allies throughout the 20th century, and Churchill was a highly respected, successful leader, so Americans trusted his opinion of the Soviet Union when he spoke of the Iron Curtain in the 1940s.