On the contrary, I think she largely does trust him, but she's also not stupid. She knows how he operates. She suspected him of keeping secrets even in 'Tec #934, after all. She reads spy novels, she's tuned into these things a bit. Genre-savvy. You notice how she didn't really seem to care what answer Julia gave? Didn't pry for an answer? I think she's just assuming Julia's a mole to be safe.Plus, it's muddied by her not trusting him, since she accuses of Julia of being Batman's Spy and so thinks Batman is spying on her in her solo.