Ok, maybe "not wanting to be associated with them" was not the right way to phrase it (I'm gonna play the 'not a native English speaker card' here in my defence).
But she explains, that she does not want to ask for their help and even declines when they offer help as she want to be independant and her own person.
Now having her appear in newspapers with them would kind of go against that, since she would then be widely known as "a Burke" and no longer as the"Sage, president of the HOTs and (probably) honour student"
And I just went to check the newspaper article at the start of all this, Sage is not named because she is not on the photo, and only the people in the photo are named. We are also only shown half of the article, maybe they talk about the adoption in the second part that we can't see and name Sage.
Soo TLDR, I did not think that "not wanting to be associated with" was necessarily a bad thing, and the argument does not really hold in the first place since we have only half the article and Sage being named in the part we see wouldn't make sense anyway
