Some general principles ;
1. The onus of proof rests on a policyholder to establish that an insured peril has occurred.
2. The standard of proof would be the balance of probabilities.
3. Balance of probabilities means that something is at least 51% more likely than not.
4. In summary, the policyholder has to establish, on the balance of probabilities, that the proximate cause was an accidental injury.
5. Proximate cause means the active efficient cause that sets in motion a train of events resulting in a particular occurrence.
6. The insurers have actually created the contractual definition of what they mean by "accident" as per post #1.
7. Check the contract wording to see what provision there is for dispute resolution. Some insurance contracts may not be within the Ombudsman's
remit or you may be obliged to submit to arbitration.
The policyholder has to show, on the evidence, that an insured event has happened.
The veterinary evidence is weak as it is ambiguous.
Evidence consistent with an assertion is not adequate proof either.
You would need a vet to be able to say that, in their professional opinion, the injury could only have been caused, as a matter of probability, by an accident. The vet is being honest in their opinion.
A second opinion, to the contrary, might be required.
Sorry if this is unhelpful. You can still push this a bit further without risk of legal costs.