[AtlUmpSteve]

Let's add the ASA Umpire manual, which states (Pregame Ground Rules),

Check the lineups from the respective teams. Make certain each checks his lineup card including first, last name, defensive position, and number of each participant. When returned to the umpire, the lineup is official. If an extra copy is available, it should be turned over to the scorekeeper.

Following the pregame discussion with the managers, it is advisable to double check the data with the scorer .....discuss with the official scorer such matters as how YOU will be handling the appearance of pinch hitters and substitutes. This matter is particularly important because of the reentry rule, and in fast pitch games, the designated player rules.

And, finally,

The umpire is responsible for the batting order and should maintain a lineup card throughout the game.