I saw that video a few years ago. It's a hoax, made by an ad agency for a gatorade commercial that never made the air. Look at the leftfielder's nonchalant reaction to the ball, which the doctored video shows as close to the foul line. Also, as she's running to her chair the leftfielder catches a baseball from beyond the foul line.

It's a fun video though.

A similar hoax video of Evan Longoria snatching a batting practice line drive barehanded before it struck the head of a woman interviewing him was another ad that never made it as a commercial.