Are the cases where people make a common mistake, but are quickly able to fix it, counted (such as forgetting to fizz and buzz for certain numbers).
What about cases where the people can code the algorithm, but can't do everything to get a program that will compile. For example, using Visual Studio with C# means some of the basic scaffolding is almost always generated and thus many developers aren't able to recall what that scaffolding is off the top of their heads.
Or is it limited to cases where they just sit there staring at a blank sheet of paper not sure how to proceed?
http://blog.codinghorror.com/why-cant-programmers-program/
http://imranontech.com/2007/01/24/using-fizzbuzz-to-find-dev...
My reading is that the scaffolding isn't the problem, writing that loop and conditional, within the margin of error of what compiler errors / an IDE can tell you to fix, is the problem. So essentially yes, they're staring at a blank sheet of paper.
My takeaway from the fact that you don't need any particular formal education to get a well-paying job is that the tech industry hires and pays people without regard to ability.
Like, the entire reason FizzBuzz has gotten popular is that it's not just possible but common to have the résumé of a senior developer (i.e., to have held all the jobs you'd expect a senior developer candidate to have held and be paid for those jobs, i.e., to have passed multiple tech interviews) and be unable to write it. You can argue about whether "privilege" got these people in the position of being a senior developer candidate, but it certainly wasn't ability.