Didn't read that review, but I disagree wholeheartedly. In fact, Lahr's dazzling biography made me want to reread the Williams plays I knew and loved, and become familiar with the ones I didn't know that failed in their initial incarnations.
Maybe he was jealous that a fellow critic wrote such a marvelous book? I've never read his Louis Armstrong bio, but I can't see it topping what Lahr did with Williams. Williams may have had his own "stock company" from his family and life in general to reuse and reinvent, but I wouldn't call that "rewriting the same play."
I think Teachout is of the persuasion that Kazan really made Williams. Maybe Kazan organized Williams. Maybe Kazan was the "father figure" that Williams didn't have in C.C. Williams. And of course, Williams' most successful work was done under Kazan's eye...with one major exception. But I don't think Kazan MADE any of the writers he worked with, as brilliant a director as he was.