The study found that getting insurance coverage increased the use of health care, reduced financial strain and improved well-being — results that now provide invaluable guidance in understanding what we should expect from the Affordable Care Act."

Nothing Chetty says here is actually incorrect, as I said before. However, I would have to say that a vast majority of readers that know little about the actual Oregon study would finish reading this article with the impression that the Oregon study simply told us that Medicaid "reduced financial strain and improved well-being" and was therefore a vindication of Medicaid.
Clarke says that this a fair characterization of the study. I disagree. The study didn't prove that Medicaid did not improve physical health. However, it did look to see if there was any evidence that it did in any significant manner, and they did not find any. That result does matter. 
Clarke is wrong to say that we should just leave out that part of the study. It may not prove that Medicaid doesn't improve physical health, but it does tell us that a study that apparently was large enough to allow us to conclude that Medicaid brings about significant improvements in financial strain, mental health, and self reported health was not able to detect any significant improvements in physical health.
That does tell us something about Medicaid. And, it is not unambiguously positive. An economist of Chetty's caliber writing about why economics should be considered a science should have made a stronger effort to convey this point. After all, that's what any good scientist would do.