The Braves probably use outside counsel for these arbitrations -- they used to use a big name out of California, so rest assured they are paying significant fees to go fight over this money.
You are right that the file and trial is a strategy the Braves have chosen and the intention is almost certainly to pressure players and to depress salary.
I just don't like it was over so little money, but the Braves have always been a team anxious to do their best to keep down player compensation -- thus their old unwillingness to sign above slot.