I'm a Mets season ticket holder, but I checked out the Diamondbacks' website for you, and here's what they have to say about it:
Chase Field opens one and a half (1.5) hours before each game Monday through Thursday and two (2) hours before each weekend game. Guests are encouraged to arrive early to enjoy batting practice, infield workouts and pre-game ceremonies. There will be some dates during the season (generally when a day game follows a night game) that the team(s) may elect to skip batting practice, infield practice or both.
http://arizona.diamondbacks.mlb.com/...ontent=guide#G
I infer from the above that the answer to your question is: no, batting practice is not reserved for season ticket holders only. What happened, or what did you read or see, that caused you to think this might be the case?
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