This is an amusing story, but it's not accurate. America just lacks the British size distinction between rocks and stones, and someone (likely a Brit) made up this explanation as a way to poke fun at Americans.

After all, when it's time for a proper riot no one really cares about the subtext of the name of the thing they're chucking. "Hey, share some of those stones with me, I bet I can smash that cop's windshield." "They're rocks, Jake - we're anarchists, not perverts."