The real answer is that both techniques should be used together, rather than favoring one over the other.
Exactly.
You can verify various primary sources against each other.
Assuming the researcher is honest, free of bias, and puts in the work to find multiple primary sources. This further assumes those sources exist, are honest, free of bias, and findable.
Obviously, a drawback of this style is that it is much more demanding of the researcher, and that there will be times when the record is unclear and you can't comment- and, again, I think Peterson does a great job of saying when the record is incomplete or contradictory.
Well, you can comment. You use interviews with people who were there. You simply note that they are testimonials taken decades after the fact.
To me, this is infinitely preferable to relying on people recounting stories after more than forty years. Is it possible that the contemporaneous sources aren't correct? Sure. But the contemporaneous sources have the major advantage of being ... contemporaneous. Unaffected by the passage of time. Of accurately recounting events of that time- as opposed to what people say decades later.
This assumes contemporaneous sources are objective. They're not. They're written by the same people who you're worried are biased. That bias doesn't go away simply because of timing or writing it down.
Hindsight is 2020. A lot of things seem amazing at the time only to find out later they're terrible. Pick any one of the thousands (millions?) of ready examples.
Simply put, it is beyond bizarre for someone to say that there is more intrinsic bias in using contemporaneous primary sources than there is in asking people to recount their personal experiences from decades ago.
That would be bizarre. Good thing that's not what I'm saying. But I'm sure you know that.
But again, you can see the advantages of this when you're looking at, inter alia, Game Wizards. It is much more instructive to see how Gygax and Arnerson wrote about each other at that time than it would have been to get an oral history from them 40 years later, when both would have been motivated (to the extent that the accurately recalled all the events) to shade the history in ways that flatter each of them in the present.
As opposed to how they might flatter each other while in a fresh business agreement? That's partially the point. Humans write the primary sources. They're no less biased simply because the information is written down contemporaneously as opposed to spoken, even if years later. Could they could develop a grudge over the intervening years, sure. But they could also have layed it on thick back-in-the-day because they were hopeful of good business dealings.
My point is simply this: information does not become objective simply because it's written down by someone at the time. Read any two history books on the same topic by different authors and you'll quickly discover that there is a lot more...flexibility to how history is presented than most people like to admit. I'm not saying Peterson falsified anything, only that his bias is clear. He favors primary sources to the exclusion of testimonials. You may be fine with that, but it's not a complete history of the topic. As said by dustyboots, you need both primary sources and testimonials to approach something like a complete history of any given topic.
As an aside, I've read history books about the Great War that got the date of Archduke Ferdinand's death wrong. I've read history books about how awesome colonialism is for the colonized. I've read books about the history of Mexico that somehow fail to mention the Mexican-American war. History is only as accurate as the people writing it choose to, or are able to, make it.
Note: We might also be caught up in using "primary sources" in different ways.