A fan asked me this.  Apparently some mistake us broadcasters for rules experts.  
 
Runner on third, less than 2 out.  Fly ball to right and the right fielder has a good arm.  If the runner on third were to go a few steps toward second and get a running start to third, then tag third and head for home after the right fielder catches the ball, would that be legal?  Instead of leaving from a dead stop, R3 would have momentum going and step on third just as RF catches the ball.
I said I had no idea but would find out.   What say you?