At the end of the section we see that the reasons are geared towards keeping the camp holy so they can win, not sanitary.
The Cheyenne of North America are the only group I know about in this regard, and I don't know anything about their potty habits. But this "keeping yourself holy" was very important in war for them. They had to abstain from sex, they had to have a cross-dressing warrior among thei number - all sorts of rules had to be followed, just like in Deuteronomy.
Hiding your poop is also just good basic guerilla warfare practice - helps avoid detection by the enemy.
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