Debunking Debunking Cyclomatic Complexity

Over at SDTimes, this article by Andrew Binstock contains a claim that this result by Enerjy somehow "debunks" cyclomatic complexity as an indicator of problems in code. He suggests that what's shown is that for low complexity of methods (which is overwhelmingly the most common kind of complexity of methods) increasing complexity of methods is not (positively) correlated with the likelihood of defects. Binstock suggests that:
Not so. What Enerjy say their result concerns is:
the correlation of Cyclomatic Complexity (CC) values at the file level [...] against the probability of faults being found in those files [...]). [my emphasis]
It's interesting all by itself that there's a sweet spot for the total complexity of the code in a file, which for Java pretty much means all the methods in a class. However, Binstock suggests that
[...] for most code you write, CCN does not tell you anything useful about the likelihood of your code’s quality.
Which it might not if you only think about it as a number attached to a single method, and that there are no methods of high complexity. But there are methods of high complexity—and they are likely to put your class/file into the regime where complexity is shown to correlate with the likelyhood of defects. Watch out for them.