Aww ... c'mon.
Rule 2.00 also says:
A STRIKE is a legal pitch when so called by the umpire, which—
(a) Is struck at by the batter and is missed;
(b) Is not struck at, if any part of the ball passes through any part of the strike zone;
(c) Is fouled by the batter when he has less than two strikes;
(d) Is bunted foul;
(e) Touches the batter as he strikes at it;
(f) Touches the batter in flight in the strike zone; or
(g) Becomes a foul tip.
So using your logic, if the batter swings and misses and the umpire doesn't actually call "strike", it doesn't count as a strike?
You might be sellin', but I ain't buyin'.
Scott clearly signaled "time" which is the same as calling "time".
(I've got no dog in this fight. I'm a Cubs fan. Come to think of it ... I guess that means I have no dog an any fight.)