Honestly, it can be biased. Noting Oren's history as an ambassador to the US for Israel, there's is to be expected a certain level of bias in what he says. However, much of what he says is also reinforced in many other works, including Randolph Churchill's "The Six Day War" (also a pro-Israel bias), "The Six-Day War: A Retrospective" by Parker (which is pretty unbiased, I'd say, since it's more of a panel discussion), and some articles. The overall conclusion is one I'd agree with, and have written about for some of my classes, in saying that the pre-emptive attack was justified and the conclusions as to why Israel won. That said, to see the other side you can check out Riad's "Struggling for Peace" (note, this is by the Egyptian Foreign Minister at the time), or check out Roland Popp's article titled "Stumbling Decidedly into the Six-Day War". One of the problems with the coverage of the war is that many Arabic sources are unwilling to talk about it, because it was such a stunning and humiliating defeat, and most that do talk about it are more willing to take on exceptional bias to make their point as such. However, reading those (I'd recommend Popp's and Parker's to get a really well-balanced view) should help.

I also did a write-up on the origins of the war in another thread, if you'd like to read that, which draws from all of these sources and more. However, it's some 60k+ characters and 7 posts or so long, so I don't know if you'll find it that interesting. Let me know!