... But I haven't an answer for you that I can support. My dishwasher is on the right side of our double sink. The disposal, however, is on the LEFT side of the double-sink. Hence, the drain for our D/W goes right through our cabinet under the sink to the disposal. (It's a 'soft hose' so it's kinda out of the way.) Why it was done like this, I donno.
Maybe it has something to do with the S-trap. I'm sure someone on the Forum has the answer. I just wanted to show you that my situation is the same as the one that's being suggested to you. I'm interested on the answer and explanations too.