Alright, thanks for the great explanation. But if the check valve doesn't fail, there is little to worry about, right?
Let's say the sink drain is clogged...which I'm willing to guess happens more often than a DW check valve failing...the DW tries to drain into the trap (or first the disposal), and can't. So, it backs up and flows out the air gap, which then flows into the sink and then is stopped again by the clogged drain. The sink fills, and spills everywhere until the DW is done draining...and until it goes into it's next drain cycle. How does the air gap help that situation?
In my "non-failing" check valve hypothesis, the DW shuts off if it can't force water out the drain. This, to me, makes much more sense than having the above scenario play out.
This actually happened to me...and that's how I know my check valve works! Turns out the connection to the garbage disposal was clogged. But the same would have happened had the sink drain been clogged.
Anyway, thanks for the knowledge!