Luke proves this wrong by reminding her of Leia training her, regardless of her heritage, showing that the value of others is determined by their heart, not their heritage, and convincing her to face Palpatine and determine the fate of the galaxy, showing that it is not her heritage that determines her future, but it is she, herself, who determines it.
This reminds me of something. Leia always having known she was a Palpatine specifically would never really work imo, even if they had the perfect footage/lines for it. It just comes out of nowhere and it isn’t explained how exactly she came to that conclusion - especially since Leia was never even in the presence of the Emperor.
I think what would have gone over better would be if Leia sensed a “raw strength” in her lineage, kinda like Luke did on Ahch-To. That way, she still realizes she is taking a risk by training her, but does it anyway because of her spirit and heart.