By Humeyra Pamuk, Jana Choukeir, Ahmed Tolba and Steve Holland ZURICH/DUBAI/WASHINGTON, June 21 (Reuters) - Negotiators from the United States and Iran were set to start peace talks in Switzerland on Sunday, even as U.S. officials disputed Iranian claims about closing the key Strait of Hormuz. A high-level Iranian team arrived in Switzerland for peace talks with the U.S., Iranian state media reported, as U.S.