If they went to court and sued for the apple they would have an opportunity to present their cases to a judge and jury and there would be a determination as to who had the better claim, on the balance of probabilities.
By the time the trial took place, the apple would be rotten, even since the subject matter was perishable and time was of the essence, the subject of their dispute would be gone.
If a trial took place, the damage to Jane and Joey's relationship would likely be irreparable, there would be significant legal costs and investment of time by the parties.
If the case was appealed, the monetary investment and expenditure of time would be extended. In addition, the remedies available would be limited to monetary compensation, therefore, if the apple in question had value to the parties that could not be compensated or measured by money, then the relief would be inadequate.
A judge, chosen by the civil courts, and not agreed to by the parties, would govern the process, and the matter would be administered according to the rules of court.