Don't quite understand why she didn't give him a clearance. He said he was going to Henderson and she acknowledged that, how did she think he was going to get from his present position to Henderson? That being said, she never did explicitly clear him so he was wrong to continue forward. My guess is if this ends up as an action against the pilot, it will be for failing to exit the class B airspace when told to do so. To the controller, a warning to use better verbiage, either issue a clearance or make sure the PIC confirms they do not have clearance to transition the B class airspace.
What's the point of an open door policy if inside the open door sits a closed mind?