Poor programmers can make a program achieve its objective, however when you read it, its sloppy. There are many twists and turns, which indicate the programmer did not fully analyze the process before coding, so they had to add in the pieces they originally neglected. This makes the program error prone, hard to maintain, and in some cases it performs slowly.
A master will fully analyze the problem the first time and design a complete solution, then commit it to code that is clean, logically well organized, it will be reliable, maintainable in the future, and perform well.
It's like the difference between a Grandma Moses painting and a da Vinci, both are paintings, but there is all the difference in the world.
There is an aptitude to do this, and it comes from intelligence, practice, refinement of the art over years, not a college degree.
I suppose there are other disciplines like this.
Regarding Scott Walker, I will look at real world results. I don't care if he has a degree, I want to know what he has done, is his success due to things he has done, or was he just standing there when something good happened and is he taking credit he does not deserve. You have to look below the surface, the devil is ALWAYS in the details.
Edit: This is not to say that all the best programmers don't have a degree. Some of the best do have degrees, and some of the advanced theory they learned in college can help them design a superior solution that a non-degree programmer would not achieve. I would never say a degree is worthless. This difference would emerge in high value pieces of code with high use, such as an operating system design, or building a new database manager to store and retrieve data, very large, complex, high use programs. For standard meat and potato applications like an accounting general ledger, you probably could not tell the difference.