During the latest hearing, Dame Victoria Sharp, sitting with Mrs Justice Hill at the High Court in Manchester, said Cox had been waiting for a shop to open at about 06.30 BST when he walked past Det Ch Insp Mark Whittaker and later two women.
The detective, who was out for a morning run, carried on past Cox after “making his disapproval known” but then turned around to arrest him.
Dame Victoria said Cox did not say anything to the women or interact in any way and “behaved in a respectful, calm manner” during his arrest, while Whittaker “was not prepared to look at the guidance”.
At a hearing in April, Cox’s lawyers argued the previous judge at Chester Crown Court was wrong to find his behaviour was disorderly.
Rejecting this, Dame Victoria said: “To walk completely naked on a quiet path used at that hour by people walking alone to work, who had no reason to expect to encounter him, no opportunity to avoid him and no-one to turn to, was conduct the court was plainly entitled to characterise as disorderly in the ordinary sense of that word.”
She added: “Far from being a conclusion which no reasonable tribunal could have reached, it is difficult to see how the court could have decided otherwise.”