I doesn't sound like it is he is trying to mark his territory to me if he only does a little wee when out,you would be stopping constantly if he was marking his territory
I think it is just down to perserverence praise him when he goes where you want him to and just give a firm "no" and move him to the newspaper when he does it on the rug.
He will eventually get the message but it will take time
Sharon,Charley & Melody xx