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Bare Hands and Dex/Balance
Just because that's your interpretation of it, doesn't mean other people should interpret it the same way. (In fact, they shouldn't)
The two lines you quoted aren't redundant since they refer to two different things: your base balance when you've got no weapons equipped and what base stats are and what they're affected by. Again, not redundant.
Your first quote is listed under dexterity because balance is affected by dexterity (ignoring other modifiers).
Your second quote is under stat modifiers because...it's referring to stat modifiers, and that equipment also modifies base stats.
What you're trying to say is unequipping weapons is the same as equipping bare fists, which, while ignoring the logical issues and confusion that goes with that statement, is just semantics.