I actually haven't read the whole [Baicker et al. NEJM Oregon Medicaid Lottery] paper, but I have read the abstract and a key table cut-and-pasted by Kevin Drum. It shows a more than four-fold increase in diabetes diagnosis due to Medicaid availability. This does not correspond to statistically significant decrease in the fraction of people with high hemoglobin glycosylation. So the paper does not contain proof that current therapy for diabetes is better than nothing.
But we have plenty of data which prove that.
The principle of extreme scientific caution prevents the authors from arguing that a higher rate of diagnosis of diabetes due to a lottery must cause better health. That is a theoretical argument, based on pooling their data with decades of data on diabetes treatment, [which they do not make].
The combination of ultra-extreme caution, the Neyman-Pearson framework, and people who are willing to describe a statistically insignificant difference as "no different" http://wapo.st/120aFds (note that's WonkBlog -- our nation's finest news source (non-irony alert)).
The commentary on the article, definitely including Cowen's, demonstrates complete statistical illiteracy. Failure to reject the null in spite of large point estimates is not evidence that the null is true.
I'd say the case for Medicaid expansion is somewhat stronger.
In fact, I'd say that any honest sane person of normal intelligence has to accept the demonstrated fact that Medicaid causes improved physical health after reading Table 2 of the paper (replicated here http://www.motherjones.com/kevin-drum/2013/05/followup-medicaid-probably-does-improve-health-outcomes-after-all).
I shall assume that sane people of normal or higher intelligence who contest this claim are lying scum.