I found the Burning Man story interesting. I understand it was a 6 mile hike in the mud for those that decided to walk out. That sort of reminds me of what we did every morning before breakfast during my Army basic training days. Not saying it was fun. Just that it is not exactly earth shattering or life threatening.
That was assuming you couldn't or wouldn't just wait it out. These days, and I am sure the same might apply to most of us reading this, I can't image not always having sufficient non perishable supplies on board to last a week of so. Water would be my big concern until it was dry enough to drive out. Those chemical out houses not being emptied? What many of us call composting toilets can be whipped up with meger supplies. Buckets and bags for solids and in those conditions I don't think disposing of urine would be much of a issue.
IDK, maybe I am just not being sympathetic enough, but I think those of us that are or have experienced the nomadic life would be far better prepared to deal with this than your average S&B denizen.