(Or, actually, this is more of an anti-conspiracy).
Commuter rail cars have doors on both sides, because on some stations you exit to the right, and on some - to the left. However, there's often no need to differentiate which side of the platform the train arrives at.
Clearly, it may be more convenient to do one way or another in a city streetcar system:
- stations raised above the ground have one platform, trains arriving on two sides - this design needs only one set of elevators/stairs down to the street level;
- stations that are on the street ("stops" would be a more appropriate name for those) don't need any special ways to get from the platform to the sidewalk and therefore the platform is on the right side of the train.
However, inter-city commuter rail systems, like BART, usually don't have a stop just in the middle of a street - not only because such transit systems usually require a huge parking lot, but also because a 9-10 car train would create quite a traffic distraction if being let loose on the open street. So, as BART stations are already full-fledged stations, using up a lot of land, it would seem strange that some stations have one platform in the middle and some - two on the sides.
Therefore, as it would have been easier - and cheaper! - to build each and every station more or less a copy of others, I can only conclude that varying station layout is intentional, and, as the side of the upcomming exit is not announced, I can only conclude this is done to catch spies. See - a local would know where the exit is, while a spy, no matter how good he is at blending with locals, would not. There are cameras right above each exit on BART, so interested authorities can monitor those who hesitate, or prepare to exit through the wrong door, and then do a background check on them. It's OK if that was just a guy who moved into the area recently, but if that was a member of a foreign diplomatic mission, who is, according to the official consulate's schedule, supposed to be at a trade meeting in another state, then something is obviously fishy.