I am convinced there exists something we can call statistical literacy. Unfortunately, I don’t yet know exactly what it is, so it is hard to write about.
One thing is clear: it is not about knowlege of statistical tools and techniques. Most of the statistically literate people I meet don’t know a lick of formal statistics. They just picked up statistical literacy from … somewhere. They don’t know the definition of a standard deviation, but they can follow a statistical argument just fine.
The opposite is also possible: a few years ago I had a formidable toolbox of statistical computations I was able to do, but I would be very confused by a basic statistical argument outside the narrow region of techniques I had learned.
In other words, it is not about calculations. I think it is about an intuitive sense for process variation, and how sources of variation compare to each other.