How is it hand waving? It's literally true a large corporation can fire a customer support agent while sponsoring a software engineer, it is not interchangeable talent
I've worked with several excellent people in my career who progressed from customer support to QA to QA engineer to software engineer.
It's not common though, and I don't think it's a case of "training". Some people have the drive to figure that path out, and those people should be encouraged and supported.
Not everyone is interested in programing. Some people are amazing at customer support and super extroverted and seek out jobs where they interact with customers and would be miserable looking at code all day. The opportunity should be there, but some people are just never going to be engineers. Management quality can't fix that.
Actually, let's think of it as a stew. Lots of different base ingredients, add seasoning and heat. When the individual bits are delicious they start bubbling up to the surface. Not every bit is a carrot or chunk of meat. Some are potato, maybe that's a bean.
I'm sorry but this is just absurd. Not everyone has the same aptitude for every job. For a company or country to function you have to acknowledge this and put people in jobs suited to their natural talents.
I doubt that's the argument they're making. They're saying they are laying of a software engineer in one org, and hiring another software engineer in a different org. Not cross functional roles.
Talent can be trained, less across jobs (although it's often what public services ask to entrepreneurs in some European countries), much more across departments.
