I think the article is trying to encourage you to realize there is a lot more practical steps you can do to map out the space of possible paths forward (which is of course also one way of making headway), than many people realize at first.
I run into so many "IT" people that dont do that step at any stage. Google has made people lazy.
I think problem solving mechanics or structure can be taught. Creativity in problem solving is probably less teachable.
For anything non-trivial, I think a process or structure for problem solving, knowing that you probably won't solve something on the first attempt and need iteration, and basic project coordination skills are needed. I think all of this can be taught.
I think there is a lot more in common across fields than people are willing to admit. There are different techniques and language used to accomplish the same thing, but it's all in service of the same underlying goal.
>I think problem solving mechanics or structure can be taught.
I'd be very interested in seeing a course like this. I know many people that need it.
My background was in automotive manufacturing, so everyone was trying to copy what Toyota did. If you excuse the obvious oversimplification, Toyota used approaches from the Training Within Industry (TWI) program  to develop internal training. Art Smalley has numerous articles, videos, and documents available ranging from TWI to problem solving at Toyota . Art Smalley shows there is a sort of hierarchy of different problem solving approaches depending on if you’re dealing with a machine stoppage on a manufacturing line all the way up to determining new markets to enter.
TWI is broken down into job methods, job instructions, job relations, and a problem solving segment. It does tend to be heavily focused on manufacturing, so you’d need to change the examples for your needs.
I don’t think there are any real secrets in the training programs. Almost all of the process improvement / problem solving methods I’ve come across seem to be a variation on the scientific method with catchier naming.
Generally two challenges I’ve seen in problem solving are people jumping to solutions directly without understanding the problem, and making multiple changes simultaneously or in sequence and losing the ability to determine cause and effect.