It is not a shortcoming of statistics that other people, like various scientists who aren't statisticians, don't know how to use or properly interpret statistics. It is a shortcoming of their knowledge.
It is not a shortcoming of the Copenhagen interpretation of quantum mechanics or the Chicago school of economics if I don't understand or know how to correctly interpret their results. It is my shortcoming and fault for not knowing enough to connect the dots.
I do statistical research some of that is through interacting with researchers in the biosciences. Often when I go to talk to a researcher and ask them if they could use some statistical or mathematical or computational assistance with their research it has almost always been a fruitful starting point to long conversations and getting into the research. Now sometimes it was simply a matter of looking at their F-test results or ANOVA scores and telling them what it meant (like with a regression model relating proportions of certain characteristics between taxa), more useful interactions for me often mean working on new algorithms or estimators or working with fitting a model from their empirical data because there isn't a reliable standard model to work off of (like intergenic distance between genes in an operon) that kind of challenge makes less engaging work worth the hassle. Maybe I'm odd because I've worked hard to have a good background in both statistics and biology, but I shouldn't be.
Although here is an observation that perhaps supports some of the intent of the article from my own experience. I was speaking with a biology graduate student and it came up that they had a biostatistics course in the department. Of course as a statistician my mind goes towards survival function, failure rate, life tables, censored data, bioassy, epidemiology, microarrays, clincal trials, topics along those lines. It turned out their course focused z tests, t tests, f tests, confidence intervals, point predictions, least squares regression, multiple regression, ANOVA, and things along these lines just with simulated problems in a lab setting. That is not necessarily a bad thing, but much of the core math was under played or missing like model assumptions and alternate formulations or things like dummy variables. The worst part was that even though they were doing well with the class they had no confidence in actually using the statistics and didn't understand how to interpret the meaning of something like a confidence interval, they knew how to calculate one, but it wasn't clear what it actually meant to them.
The corollary to the notion in the summary I'd rant and claim is that scientists overall have less than desirable skills in mathematics, statistics, and computation than those who studied those disciplines principally and that's hurting science. However many in those three disciplines really know little beyond basic results in any of the sciences which hurts the applicability of these mathematical fields to the sciences and likely hurt our ability to develop certain types of discipline specific results that can be generalized from work in application problems.
In either case whether you're a typical scientist or a typical math/stat/comp person in order to become proficient enough in the other areas it requires going an awfully long out of the way compared to any counterpart who simply does not care and goes straight through as many before have. While in some areas of research on either side it is no problem to do as has been done and not further knowledge into those other areas. Increasingly results that have the highest levels of impact are coming more and more from truly interdisciplinary research. In order to further encourage that for those who are interested in such fields (aside from making more clear what areas in any of the fields fringe to such interdisciplinary work) we need more incentive to study more than one field and/or better ways of enabling fruitful cooperation between the camps.