What exactly does compelling evidence mean?
Evidence is straightforward. It is material which supports the case that a particular state of affairs exists.
But compelling evidence? Does this suggest that the case is not strong but with a little effort or twist could be perceived as being stronger?
I think it is supposed to mean that the evidence does not prove the case but suggests that it is correct.
As a thought experiment, not suggesting that this was the actual case:
Suppose you have a group attending a meeting that was leaked to a reporter after the meeting. You decide to check the call logs on the phones of all the attendees.
Most hand over their phones one objects strongly but eventually hands theirs over.
On the phone of the objector you can see that they phoned the reporter right after the meeting.
On some of the other phones you see that the reporter has called the owner after the meeting, but after the call to them by the person that objected to phone checking.
Such a sequence of calls record cannot possibly prove the identity of the leaker, but can be regarded as compelling in as much as it would destroy confidence in the suspect.