Probably the biggest obstacle to understanding Peterson's conception of "truth" is the word itself. If you ditch that and replace it with something like "wisdom" (which he does himself in the second part) you'll have a much easier time making sense of the first podcast, which is centered around a contradiction that neither speaker could properly elucidate until later on.
Peterson's wisdom is better understood as a commitment to a worldview, as opposed to the traditional notion of truth as a property of a proposition. Given these two distinct definitions you could imagine a situation where the truth value of a proposition was in conflict with the broader commitment to a worldview.
Now I'm open to other interpretations here because I'm pretty drunk and writing without reviewing the videos, but it was my impression that Peterson assumes the default commitment to wisdom for humans to be fundamentally Darwinian, that is, concerned with human survival. He compares this to the more sterile Newtonian worldview which operates under the assumption that things are essentially composed of matter and are able to be perceived and classified as such (note that the Newtonian endeavor itself probably has Darwinian origins). But the Darwinian worldview, moreso than the Newtonian one which is more or less indifferent, introduces a telos (end goal) for people that permits a moral realism - or the classification of moral claims as objectively true or false.
So under this system, if a person were to authorize the use of an atomic bomb or other weapon that was potentially hazardous to the whole human race, they would not only be doing something wrong but also enacting an ethical value that is untrue as a result of its incompatibility with human survival - even IF that action were justified through a system of otherwise true propositions.
Where Peterson and Harris disagree is that while Harris is also a moral realist, his moral realism is founded on a utilitarianism that he sort of grabs out of thin air, as opposed to one grounded in Darwinism.
I have some objections to Peterson's position here, but I think he's coming from an interesting place and aware that his position is a minority one by a large margin, which is why he seems to take the more "humble" position through the first podcast. He knows that Sam is arguing from the commonly accepted standpoint and is capable enough of pushing that argument to where it would be difficult to counter, despite the fact that he isn't a scholar or otherwise qualified philosopher.