I just don't think the two accounts disprove each other.
You gotta wonder why Charl would step up with that story.
Usually the truth is somewhere in between but it does seem like, at least according to Chael, that he didn't just run out, that their was communication prior.
Chael also said the way it all went down for him was weird and understood how Wand would think so too.
I could see Wand looking at the situation and thinking, well I don't know who this guy is, and I'm going to fail this test anyway, and they may not even have jurisdiction, so I'm gonna just split.