I worked in a job that seems to match the description of computer network architect in high school. It certainly required a fair amount of self-teaching (in my case; I suppose one could replace that with college or on-the-job instruction). Knowledge provided by a source of some kind was necessary. One is typically not born knowing how to do that type of work.
Does a job that does not require teaching (self or otherwise) even exist? I have family in the manufacturing business that I occasionally help out with when they are short-staffed as a favor. From the outside the job looks about as menial as it gets, but actually stepping in and helping leaves me appreciating what those people are capable of doing with the knowledge they have. There is no way, with my limited knowledge and ability in that industry, I'd be hired to work for them if they weren't desperate.
I farm on the side and that is the most intense ramp-up of knowledge requirements I have ever experienced. That experience has been like learning CS and software engineering, forgetting everything you learned, and repeating several more times. And still feeling like you don't know what you are doing. I've been farming for 10 years now and I still feel like a newbie. After 10 years of software development, while I recognized that there is still more to learn, I at least felt pretty confident in having progressed in my knowledge and abilities to a more advanced level. I don't know that anyone who claims farming requires a degree.
If degree here simply means requires an education of some kind, not specifically a degree from an accredited institution, then I'm not sure that there is a job out there that doesn't match that description in SV, the mid-west, or anywhere else. The only explanation here seems to be the expectations of employers, who trend towards setting more arbitrary expectations as the competition for the work increases. If you only have one applicant, you simply can't be choosy about who you hire.