Plausible Deniability
Three people in a public restroom is a chorus. Two people in a public restroom is a standoff.
You're browsing emails atop your porcelain throne. You chose the stall furthest from the door, because -- we never know -- it's probably cleanest.
And then you hear the dreaded sound: the door opens. You double check that your stall is locked (just in case The Stranger tugs on your door, leaving you completely exposed in this all-too-human position). And just in case, you shuffle your feet forward to signal that "this stall is occupied". The Stranger accepts your message and chooses the furthest stall away from you.
At this point, all sounds are sacred. You may not particularly mind hearing the other person's lunch, but by golly The Stranger is not going to hear yours.
There's one major defensive strategy during potty standoffs: create masking noise.
- Coordinating flushes/coughs/sneezes with flatulence/ploops is a classic defensive move.
- If you or The Stranger were particularly averse to standoffs, he/she could've turned on some faucets from the sink to create some noise -- it's an uncommon, albeit completely legitimate defensive move.
Of course, The Stranger is in on the ruse too, because he/she uses the same tactics. But the goal is not to not be heard, but to create plausible deniability for yourself. Because you can't stand the idea of knowing that The Stranger knows that you know that they know the timbre of your anal sphincter.