I took his lecture course on US history from WWI to WW2. I found his lectures very informative and clear, but I also got the sense that he dismissed historical interpretations to the left of the centrist historical consensus without really considering them.
When Seymour Hersh published a big takedown of JFK in 1997, Brinkley wrote a review for I think Newsweek or Time -- I can't find it online. I was a bit shocked that he dismissed most of Hersh's accusations -- the assassination attempts JFK and RFK orchestrated, the mob connections, the womanizing -- as old news, as if the public already knew as much of it as historians did, or as if it didn't matter.
He also dismissed conspiracy theories about the US military knowing in advance about the Pearl Harbor attack. I think he's probably right about that, but as I recall, he said it without even a sliver of doubt that we know everything everyone involved knew half a century ago, and without acknowledging that the attack solved a huge political problem for the military which could have provided an incentive to look the other way -- even unintentionally.
The distinction I'm making is subtle. I've never seen convincing evidence that the Pearl Harbor conspiracy theory is correct, and I think people convinced of it are not thinking rigorously. But that doesn't mean that there is no convincing evidence of the theory, or that we know of no compelling evidence of the theory. In particular, I think institutions have a powerful way of creating convenient blind spots that let a group of people act out intentions that no individual may be conscious of. There is evidence that the military at the time not only wanted to enter the war, but desperately wanted a decisive causus belli to sway a reluctant public into full-throated support for the war. And there has been lots of criticism by military tacticians since that points out how bizarre it was for the military to assemble so many targets in a single location without preparations for defense. Does that mean the military specifically knew of that specific attack? No, but it may mean that there was a practical strategy either not to apply the normal amount of precaution, or to tempt the Japanese military into a political and military tactical error.
In short, in both of these areas, I think there is much there that a curious historian can and should engage. But Brinkley seemed to find these areas of inquiry unworthy of consideration, of focus or of respect. I think that's a mark of poor history scholarship.
But I was also looking for excuses to criticize my professors in those day... and probably still am!