3x07 showed that Dick not only trusts Kory but also that he definitely lets her get away with things he wouldn't let others.
Kory makes the decision to seek out Valeska for information knowing that it was against Dick's moral code; something he'd never do because of what happened to his parents.
When Kory tells him that she spoke to Valeska, Dick asks her if she made a deal with the mob. His tone hints at him being a bit upset that she would do that; but once Kory assures him that calling what she did a deal would be an overstatement, that's literally the end of it. He doesn't argue, doesn't question her any further, nor does he show any signs of being mad at her when they meet up later.
Prior to this interaction, Barbara made the decision to destroy Oracle because she was afraid that Crane would use him to injure/kill Dick. The decision made sense. Yet when Dick finds out that Oracle is gone, he (wrongfully) yells at Barbara and tells her she's getting in the way.
So, two decisions were made without his input yet the one he chooses to get mad at is the one made to save his life.
And this isn't the first time Dick has "turned a blind eye" to Kory's decisions and actions. Back in s1 he accused her of kidnapping Rachel but made no attempt to get her arrested. She stole his car and he made a joke about it. Then after she attacked Rachel he defended her to Donna, saying that that wasn't the real Kory (even though he had only known her for a few days).
So basically, this man is truly in love and Kory can do no wrong in his eyes.
