Dropped 3rd Strike

[Dean Strong]

I recently heard a coach tell his players that a 3rd strike that hits the dirt before it reaches the catcher (assuming that the batter swings, or it really falls off the table) is technically a dropped 3rd strike, even if the catcher catches it on the bounce.

6.09 says "The batter becomes a runner when ... (b) the third strike called by the umpire is not caught, providing (1) first base is unoccupied, or (2) first base is occupied with two out;

I know a catch is "secure possession in his hand or glove of a ball in flight..."

I guess I've always thought of the "catch" definition as applying to a batted ball, and have not considered a ball that bounced in front of a catcher but was secured by the catcher a "dropped third strike."

Does the coach have me on this one?

And since we're getting technical, I noticed the rule says "the third strike CALLED by the umpire." What if it is a swinging strike?