How would Annie's going underground prove anything? I'm wondering how Annie's going underground (in episode 23) would prove she wasn't the Female Titan? Also, was her reason for not going there only because she knew it was a trap, or did she have another reason as well? It feels like I have missed something..
The problem is that Mikasa was with them. Were it only Armin and Eren, Annie might not be that afraid of going underground. Annie knows that in human combat, Mikasa can match her if not best her. The only way for her to defeat Mikasa and take Eren with her is for her not to go underground. Going underground will prevent her from transforming, not because of the dark, but because if she transform there, she will be trapped in the tunnel, preventing her from moving. Being unable to move will cause not only:


her identity as the female titan be exposed
be captured by the Scouting Legion
failing her mission of capturing Eren alive


that's why.