GFCI Problem with Three-Way Switch WAS Two Switches Neutrals Only, Switched Hots Not Used
From your description it sounds like you have the intelligence to understand this stuff, but are simply lacking certain nuggets of information.  You'll want to read up a lot on "switch loops" and particularly "3-way switches".  It will all make sense pretty quickly, then.   

Oh, and one more thing that's a bit harder to uncover:  In America, wire colors do not have firm meanings.  Green always means ground.  White or gray always mean neutral, unless marked or in switch loops and messengers - the goal being to build the necessary circuits with readily available multi-wire cable even though it's the wrong color.  "Hot" lines are everything else - including marked whites and (implied) switch-loop whites, and there is no official standard of how to designate certain types of hot. (however in commercial facilities, consistency is required.)