We have been playing with everything on the table, open information between GM and players.  This particular player has a hidden trait only in the sense that it is subconscious and internal.  Her sadism doesn't drive internal monologues because it is subconscious, it is a drive but not part of her thought process.  It is also not manifest in overt displays of cruelty, so NPCs don't react to it.  There's no hidden information from me, the GM, but my concern is that if it isn't a source of internal or interpersonal conflict, it doesn't add much to the game.

In practice, I might say "Why are you bringing that trait in?"  The player responds, "Because I'm hurting someone."

I think my action plan is to just have NPCs start to notice, some finding her sadism a passion for righteous justice, others finding it abhorrent.  We'll see how the PC responds, and if this registers any self-reflection for her.

My rpg group just started our first Dogs in the Vineyard campaign yesterday and all goes well so far, except for a disagreement between myself (GM) and one of the players about how Traits work.  He started to write up his Dog, and when it came to traits, his first pick was "2d8, Sadistic".  I said "Hmm, that's your biggest Trait die, so this is a really important part of your character. Is this a source of inner conflict for your her?  She is committed to being pious but takes pleasure in hurting or humiliating people?"  He said it wasn't.   He figures his character isn't aware that she's sadistic, so she's not conflicted about it.  Then I asked him what might happen during the initiation to the Dogs, when one of the teachers catches wind of her sadism?  He said he's sure no one will ever find out.  in fact, because he's all the more effective at doling out violence, the Faith would probably see his effectiveness as an asset for a Dog without examining its nature.  The other players were pretty split about this.  We got side-tracked for maybe half an hour with a conversation about sadism in religion and socially-sanctioned violence.  Another time, it might have been interesting but it really threw off our character creation momentum.

So I guess my questions are:
1. Can a Dog have a starting Trait that is considered sinful in our setting?  To me: I'm good in a fight is a good starting trait, but I like to hurt people is not.  Similarly, another PC was raised by a wealthy family.  It just wouldn't seem right to me for his highest trait to be I am Greedy.  After character creation, I know I'm not in a position to judge the Dogs, but I do disagree that this PC would clear initiation as the player described him.
2. Are Traits somethings that NPCs can always see, or can there be a 'hidden' or covert trait like this one? I have been thinking that the NPCs respond to PCs based on both their decisions and their traits.  The small town sheriff might trust the upper-class Dog less, but the college-educated steward might be happy to find someone to relate to.  I'm also worried about this Sadistic trait being used in every single conflict, from verbal humiliation to gunfighting, especially if the player thinks there won't be any fallout from this hidden motivation.

Anyone have guidance in this question?

[Edit: Breaking up what is really two distinct questions.]