Sorry - what follows is probably way too much information, but it may shed light. There are more than one or two factors involved, and the scenario which you've cited will rest largely on the quality of the evidence and the type of Policy. Aviation insurance isn't my field, but there are a few general things which spring to mind.
1. Usually if what they did didn't actually contribute to the accident, then it doesn't count. So if the pothole would have caused the damage anyway, the insurer would have to prove that the overloading actually contributed to the circumstances of the accident, otherwise it's unlikely that refusal could be maintained.
2. The policy holder would have to demonstrate that the damage for which they are claiming is an event for which the Policy provides indemnity ("onus of proof"). So if the event was in dispute (whether before or after it was paid) and there was evidence it did not happen as stated, then the policy holder would have to prove that an event which was covered by the policy caused the damage, and that it is not attributable to any other event for which the policy does not provide indemnity (see point 3).
3. Civil claims are determined on the basis of the "balance of probabilities", and there is a classic authority is a case by the name of Briginshaw v Briginshaw. Without getting too technical, it basically says that if everything logically points to the fact that it happened, then it almost certainly happened. So if there was no other possible explanation (or other explanations of the cause of the accident were unlikely) then they can refuse the claim on the grounds that it is likely that the incident occurred because of an event which is excluded under the terms of the Policy.
In all portfolios, when evidence comes up which is strong enough to indicate a revisit of the claim is warranted, you'd start looking at the following:
1. Technical evidence.
2. Paper evidence
3. Witnesses
4. Type of Policy and the indemnity it provides.
Then the whole thing is weighed up and a decision made on the strength of the available evidence.
Keep in mind that even at the end of the day, even if the claim is paid in these circumstances, it may end up with a revisitation of the terms and conditions of your policy and the risk you represent.