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."
Hm well "stones" and "balls" can mean "testicles" in context, but it's usually pretty clear when they should mean their literal definitions. If someone was "throwing stones" or "throwing balls" I doubt anyone would think they were throwing testicles.
Which to Brits is ridiculous as to them "rocks" are rather larger bits of stone that are pretty hard to pick up, let alone throw.
I'm told. Not being a native speaker of either British or American English I wouldn't know if this is true or not, but I thought the story was amusing enough to share.