I think this is overblown and repeated gospel.
People in factories are trained to work the tools and machines they work. What's the barrier for an immigrant besides language?
Shop clerk? Farm worker? Baker? Cleaner? Butcher? Driver? I have an infinite list of jobs that do not require much education and even a longer one of jobs that require it, but only on the resume.
Also, are you assuming immigrants at home don't study, nobody of them is a mechanic or electrician or plumber or carpenter?
Let's be honest: immigrants aren't less educated for western societies. It's us who have went through 20 years of studies to center forms in a web page or work as secretaries or scrum masters or bank clerks.