Gosh, that is a confusingly written article. One would almost suspect it is deliberate. Your OP is also VERY inaccurate.
But reading it closely - the person who saw him at Barnard Castle was not lying, did see him there and DC has admitted to this. The paper complains that this person broke rules by collecting his daughter from university. Two responses to that - firstly I believe that was permitted (daughter was effectively moving house) and secondly he is a private citizen and his actions are of no concern to the public.
A second person - Tim Matthews - claimed to have seen DC in Durham on the 19th. This was a lie, and although the accusation was repeated by papers not much was made of it by most people as there was little evidence.