The way he mentions that Apple HR confirms that there are 'no career paths' at Apple makes me think he's referring to a more regimented promotion system (a la GE).
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).
I've never heard anyone claim that Apple is overly bureaucratic.
Remember that 1984 video? Yeah.