Check out the clip, it's only a couple minutes long, and kind of entertaining. If you think wipes are bad in a permanent city's public sewer system, they're much much worse in a temporary city's waste management system. For those who are new to Burning Man, or just haven't ever thought much about how the potties work, let me fill you in a bit. The company that provides and services the porta-potties sends trucks around to each porta-potty bank several times per day to clean and service the potties. To get what's inside the potty out, they use a high pressure suction hose that's about as big around as a ping-pong ball. Anything that doesn't break down and dissolve easily in the blue funky goo that's in the potty can wind up clogging that hose, which means the team has to stop and unclog it before they can continue. The more delays they have, the longer that each potty on that vehicle's route has to go between being cleaned and serviced.
You can bring and use wipes if you like, just make sure to take used wipes with you back to camp, and pack them out with the rest of your other trash.