I don't think I agree, given the motivations and actual practices of burning are both unknown. They mention burnt homes, indicating they're aware of the practice, but steer clear of including in their study. IMO that makes the most sense because while House Burning (which may or may not have been done en masse) could be related to egalitarian home size, it's not clear that it is related; and if it is related, it's not clear at all what the relationship would be.

The only value of tying the two things together would be saying "We don't and maybe can't actually know anything about these people," which is useless. Instead they took a focused approach to using a known tool, the Gini coefficient, to make some specific guesses.

Lice is my guess as to why the houses were burned down—that or spiders.

Or bed bugs :P

How often did towns burn in the written history? Closely packed wooden structures are prone to fire — nothing remarkable

You can find your suspicions answered pretty quickly in the linked Wikipedia article.

The page mentions various explanations (just-so stories that are expected for archaeology). No definitive answer.