This is probably what he means. It's the case at a lot of companies, and particularly tech companies. There's probably no set rulebook along the lines of "You will spend X years in Y position in Z department, then you will be promoted to Y+1, where you will spend another X years until Y+2," etc.
That kind of structured progression seems to be going away in a lot of industries, with the notable exceptions being the big client-facing industries (consulting, banking, law, and so forth).
If you look at company reviews on glassdoor.com, you'll notice that people either complain that their company has too many layers of management, or that there are no opportunities for advancement.
I've never heard anyone claim that Apple is overly bureaucratic.
That kind of structured progression seems to be going away in a lot of industries, with the notable exceptions being the big client-facing industries (consulting, banking, law, and so forth).