The underpinning of their beliefs is that they are so righteous that they believe that if their "incontrovertible facts" can bypass a Judge and presented to a jury comprised of men from the Clapham omnibus, that they would prevail.
From what I could make out, Waugh is not so delusional that he thinks a jury would be involved in his appeal, but he does think that somehow a hearing in front of a judge, as opposed to a decision on just the paperwork, will work in his favour.
My guess is that it's a matter of ego and attention. He thinks he's cleverer than any old judge, and will demonstrate that to his own satisfaction given the platform of a courtroom. The inevitable defeat will, it goes without saying, be down to judicial cheating. Furthermore, he gets attention in the court, and more important, he is able to trumpet his moral victory to the waiting masses, and gain the reward of sycophantic interviews of the type we're discussing.
To that extent, he may be being honest when he now says he always expected to lose, because it was always about the theatrics rather than the result. However, you would have thought that at least some of his following might begin to wonder about the contradictions between his position now and the much more bullish stance he was taking previously.