Most people who go to school (even up till something like elementary school) do not take up those jobs, hence the jobs do have something to do with illiteracy.
You don't need to be literate to do those jobs and so chances are, a lot of people doing those jobs are illiterate.
You don't need to be, so therefore you aren't? Sounds like a fallacy and a generalization.
But you’re right, there are exceptions, although far in between