On both sides there is a relentless pursuit of victory and all means are pursued toward that end. But the objectives are different. For Wallace– and conservatives in general– the motivation for battle is a struggle between the legitimacy of right over left. However for Stewart (but definitely not all liberals) the struggle is not between right and left but between truth and falsehood. With that in mind one can begin to see how a warrior on the first side would detect a "political bias" on the part of the other– precisely because those objectives are different. The weapons that the first faces (truth) appear for all the world like the enemy they are battling ("liberalism") and expect to be confronted with.
Jon's bias isn't 'left' so much as true to the form itself which is motivated by a desire to expose hypocrisy among the powerful, whatever its source! Jon's point could have been stated more clearly, which is that the relentless pursuit of the truth has no political bias (except that the only people who ever abuse power are the ones who have it!!) If the fish caught in that net are mostly of one party that indicates not a bias of the reporter but that abuse of power is more common in that party. It all comes down to the truth, not ideology (though Jon did a very commendable job of claiming the bias that he does show occasionally- something that doesn't help the truth though it may produce a better laugh in the moment. Political bias is never OK in the pursuit of truth, even when it's very funny!) The opposite of that approach is not 'conservative', but rather condoning deceit, and what is worse, a failure to call out those who abuse power. If he only exposed people from the right while ignoring hypocrisy from the left, THAT would be bias, but Stewart follows the noble mission of political satire– the true weapon of the little people– relentlessly.