The Dodgers are simply postseason rivals
This is a fact that often gets overlooked. The Braves and Dodgers are still considered the two best teams in the National League. As a result, the media wants to paint this picture they are competitng against one another. In reality, these two teams will only square off head to head in seven games next season.
Of course by season's end the Braves and Dodgers could be battling for the best record in the National League and the #1 seed. However these off-season acquisitions by the Dodgers don't play much of a factor in Atlanta's quest for a NL East title because they are not in the division and won't see each other often. This would be a different stroy if the Phillies made these moves.
If things play out like they should, the Braves and Dodgers most likely wouldn't meet until the NLCS and that is assuming either team is able to get past the Division series. We know anything can happen in October.