Of course programs will be worse when non-programmers are in charge of programming. That doesn't mean they shouldn't but lots of indie game attempts fail because the programmer (educated or not) doesn't have a clue about when to refactor and make sure the design of the system matches the intention of the game. You can only tinker until a certain point, after that you're just creating new bugs by fixing other bugs.

ID software once was a small team and they built complex games by writing tight code which was modular and very clear. Lots of their '3d era' contemporaries failed because their engines were sloppy, complicated, buggy and slow.