I sometimes think my older cousin acts the way she does is actually due to bad experiences. From my experience, I’ve been stonewalled from her especially when I asked her about her school experiences she either denied it, mentioned a few instances, glossing over it or stonewalling me about it (though it could’ve been far worse than she’d admit). She admitted to being mocked by her own peers over her name which she eventually got over and got along with them.
But with her own mother stonewalling her for being too emotional (she did the same to me before) I suspect her tendency towards self-sufficiency might lean from distrust and that she turned to her peers as the kind of mother she never had. In the sense that her own mother rejected her for being emotional. Assuming if she’s been encouraged by her own mother to repress bad feelings (she did the same to me), then there’s a chance her tendency to tease and gossip might be some of her more socially acceptable outlets to express anger.
Even if it risks being passive-aggressive since I know it from experience. She could be independent out of distrust especially if she’s got so many bad experiences she doesn’t want to admit (assuming if the bullying she got’s worse than she admits). It seems she might not be that well-adjusted but in the sense of being secretly distrusting at times which manifests as teasing, gossiping and stonewalling.
That her independence comes from a big place of hurt that she’s not open about.