Just how secret are they supposed to be? (Should I tell players who want to read the book to avoid this chapter for example?)
Yes, I’d tell them they can read all of the book except the awesome super secret rules.
Anyone who reads them anyway should get a Persona 
Weeeeeeeeeeeeell Thor told me to go read them, so that’s my excuse.
Why are players reading the rules for the GM? Are you going to have them read the House of the Three Squires before you run it?
That’s no fun! Let secret information be secret! Let it be discovered in play.
But I am mostly a GM. Should I ever play I now know this stuff. Can’t be helped.
Yeah, there gets to be a point where you know the stats of every monster in the Monster Manual, true, but no need to rush that…
I read them because I was GMing. But I locked them away in the part of my labyrinth brain where I won’t find them again until I’m actually running the game again.
In my experience, the players who will take advantage of player knowledge gained by ignoring such warnings are exactly the ones who’ll ignore said warnings.
But I guess my question is, if a player tries to do one of those things, without thinking about it being nature related (and worth a benefit), should I just give them a pile of dice to add to the roll?
Well you only add nature to a roll when you are explicitly tapping your nature. However, the GM always decides what the test is for, so if they describe something that goes with their nature without realizing, yes, you give them a nature roll instead of brushing it off as flavor text or giving them a test for a skill they stink at! That’s how they figure it out 
I always roll Secret-Nature-Rules-Wise before each game to see if I know them
What’s the Torchbearer Ob for that Wise Test?
It’s an Ob 4, but since wises aren’t tested in Torchbearer, I have to roll it in Mouse Guard.
Huh? I figured the Ob was in the Secret Rules section and was just trying to trick you into telling me. :?
It’s the GM’s responsibility to determine what ability is tested. If player describes an action that falls in line with the secret nature rules, I should hope that you’ll indicate that Nature should be rolled and for what effect.
-L
Tsk tsk, that’s under the forbidden Wises.
A GM can call for a Nature roll in a test? I had a GM try this on me once and I was like, “Wait, what about our skills?” I was under the impression that rolling Nature is a resource the players can call upon rather than a test that the GM can invoke.
A player can call upon nature when tapping it, but otherwise the GM is the final arbiter in what any test is. I think the idea is that the player has an idea what his nature entails so he’s more apt to describe doing something in terms of his nature, and that description is what the GM uses to determine that the test should be nature. Also keep in mind that if you have an appropriate skill, that takes precedent over nature, even if it is lower than your nature. So an elf with scout won’t be using their nature when stealthily scouting ahead to see what enemies are about even though their nature includes sneaking. However this does mean that if a player RPs an applicable aspect of their nature without realizing that it could actually be mechanically useful, the GM can jump on that and give them the test they didn’t know they were fishing for.