It's pretty common for machinists in most industries (including aerospace) to lack college degrees. Studying engineering in college typically has little relevance to operating a bandsaw. A safety knowledge test before having access to the shop is standard and common sense, not elitist.
They do have degrees, just not the one you'll get from a 4-year university. The time of getting a job at the factory right after high school is long past. The machine tools these days are quite complex and very expensive. Like 6 axis CNCs with incredibly flexibly degrees of freedom.
Also, a lot of modern machinists have, even, a basic understanding of materiel science. They might not have taken all the courses to graduate with an engineering degree but they aren't that far off.