I think her not telling Jon is more an example of Sansa's character development than any statement on her actually distrusting her brother.
All the (main) Stark kids are going through some kind of major change and loss of identity. Bran wanted to be a successful warrior and traditional kind of physical hero, and instead is becoming the epitome of the squishy wizard; knowledge and magic are his only recourses to impacting the world around him the way he wants to. Arya is literally learning to switch out her face and has become a killer with sociopathic tendencies; and it's rather important that the only sign of her old identity is Needle, a weapon, perhaps showing how even the mild amount of "proper lady" she had in her has been flushed out. Jon has died; he's literally been reborn into a new life with a new perspective in which his original goal in life is now effectively destroyed (and he may have other new identity tropes if a certain spoilery book reader equation is correct.)
Of her siblings, excluding poor, underdeveloped Rickon, Sansa's surface appearance seems to show her as the least changed of all of them. But she might be the one with the most actual changes in her character. She was a young, naive, trusting girl full of ideals and a willingness to see the best on others even when they were expressly trying to dissuade her of that (I'm looking at you, Sandor Clegane.) I wouldn't be surprised if her final form is as an ever-shrewd, highly cynical and cautious politician, with her old fatal flaw being reversed: instead of being far too trusting, to the point where even ruthless people like Cersei will spare her because she's just so harmless, she'll be untrusting, to the point where even she knows it's a major flaw that damages her relationships.
Turner gave Sansa a bit of a flinch when she lied to Jon. It wasn't just a tell to the audience; it may have been the character realizing that even though her own mental faculties want to tell Jon the truth, some part deep down inside won't let her.