When Yoko asked her how she could believe in Simon so much, and Nia's answer was "Nantonaku" which means "I just have a feeling." Basically she's saying that she doesn't have much to back up on, but she believes in him intuitively. And then she says the same thing to Yoko later when asked why she closed her eyes when Yoko was aiming at her, and that was what finally got Yoko to like her.
Pre-timeskip, Nia is well aware that she doesn't know everything about her friends, but she tries very hard to learn more, and she continues believing in them because from her observations, she thinks they're trustworthy. Even when the Great Gurren Brigade were suspicious of her in the beginning, she told Simon that she still got a warm feeling from them and thought they weren't bad people. And Simon was always there for her where her father was not. When she found out her father just thought of her as a doll, Simon told her she should just live as herself, accepting her as a human being. After all that, why should she doubt him? That's just how she views things.
Besides, she does end up losing her faith for a while when she turned Anti-Spiral, joining the hivemind and gaining all the knowledge about the Spiral Nemesis. And so Simon had to WORK to win back her faith. If he had died in prison, would that have made her believe in him again? No. It was only because he got to that point inside Cathedral Terra and was able to talk to her that she finally became her old self again.