I don't think he's confusing cause and effect. There are instances where burnout is caused by a lack of purpose provided by the job. Just because there are instances of work feeling meaningless caused by burnout, doesn't mean the inverse cannot happen.
> People who do work that clearly improves other people's lives can still feel that their work is meaningless.
I can't imagine this is common. For someone to feel this way, I feel, they probably have underlying issues of existential origin. This is assuming the person is directly doing work that is improving someone else's life.
Consequently, the yearly turnover rate is approximately 30 percent.
Most people are employed in the course of something important and/or useful, even if it's tedious or boring.
There's a strong argument that some of the least skilled jobs provide some of our most critically important functions. Those positions are low paid because there are lot of people willing and able to do them, not because they aren't needed.
I think claiming "my work is meaningless" is just a broad expression of workplace dissatisfaction and not really specific enough to mean anything. The position itself likely has an important function or no one would be willing to pay for it.
You're confusing cause and effect, to a certain degree. The feeling that your work is meaningless can be a symptom of burnout itself. People who do work that clearly improves other people's lives can still feel that their work is meaningless.