This matches my experience. In addition I was advised/strongly encouraged to "go dark" on social media and refrain from ever discussing work at lunch, even with teammates.
My badge only worked where I had explicitly been given access, and desks were to be kept clear and all prototypes or hardware had to be locked in drawers and/or covered with black cloths. Almost every door was a blind door with a second door inside, so that if the outer one opened, it was not possible to see into the inner space.
That sentence, by itself, is more or less correct (from my 26 years at Apple). However, it suggests/implies things that are not correct.
1) In case you got the impression: Apple certainly does not design software to be non-collaborative simply because it would enable sharing/leaking when used within Apple. I would say that Apple has been focused since Day 1 on a mindset where one-computer equals one-user. The mindset was that way really until Jobs was fired, discovered UNIX, and then returned with Log In and Permissions. To this day though I think collaboration is often an afterthought.
So too do they seem to be focused on the singular creative. I suspect Google's push into Web-based (and collaborative) productivity apps (Google Docs, etc.) forced Apple's hand in that department — forced Apple to push collaborative features in their productivity suite.
2) Of course Apple collaborates internally. But to be sure it is based on need-to-know. No one on the hardware team is going to give an open preso in an Apple lunchroom on their hardware roadmap. But you can bet there are private meetings with leads from the Kernel Team on that very roadmap.
That internal secrecy, where engineers from different teams could no longer just hang out in the cafeteria and chat about what they were working on went away when Jobs came back. It probably goes without saying it was rigorously enforced when the iPhone was a twinkle in Apple's eye.
The internal secrecy was sold to employees as preserving the "surprise and delight" when a product is finally unveiled but at the same time, as Apple moved to the top of the S&P500, there were a lot of outsiders that very definitely wanted to know Apple's plans.
3) Lastly, yes, plenty of floors and wings of buildings are accessible only with those with the correct badge permissions. I could not, for example, as an engineer badge in to the Design floor.
Individual cabinets needing badge access? I have no idea about that. I am aware of employees hanging black curtains in their office windows when secret hardware would come out of their (key-locked) drawers. (On a floor that is locked down to only those disclosed, obviously the black curtains become unnecessary.)