that's a completely made up statement. i have worked in lots of IT shops and the only place to find folks w/o a college degree is in the help desk/desktop support. i've came across but a handful of developers who didn't have a degree.
i've been involved in the hiring process for my companies, and the candidate's college status is a major part of the package. we expect someone to come in with "bright" eyes and to know deeply what they're talking about, not someone who can bs here and there. college only gives part of that. in addition, they need to be a go getter. the should know about code management processes, and about enterprise architectures, n-tier, etc. development patterns, etc.
Maybe you missed this part of the heading (not even TFA):
"Nearly half of the software developers in the United States do not have a college degree."
That isn't just saying not a "computer science, engineering, math, or physics" degree, it's saying any college degree at all. So, presumably a lot more have college degrees with other majors.
So how exactly is almost half plus every programmer with a non-STEM degree "The Exception"? It seems to me the STEM majors are the exception.