I don't know if you could call it "frivolous" rumor, but the rumor that the U.S.S. Maine blew up in Havana, Cuba in 1898 led, partially, to war. The rumor was that the Spanish did it and the explosion became a rallying point for anti-Spanish sentiment. The Spanish-American War began only a few months after the sinking. Later, it was discovered that the explosion was the result of a fire onboard and not mines or explosives. So the Spanish were not at fault.