No, it would be a gross misunderstanding to think ChatGPT has anywhere close to all the data possible. Not even close to all the data on the internet. Not even close to all text. Let alone data available by directly interacting with the world.
I agree with your other points, but why would you think ChatGPT was not given all the data on the internet?
If you aren't storing the text, the only thing that stops you retrieving all the pages that can possibly be found on the internet is a small amount of money.
I'm pretty certain that OpenAI has a lot more than a small amount of money.
Even the paywall issue alone, I can’t see how they could scale doing paywall signups automatically. Each paywall form is different, may require a local phone number in a different country to receive a text, etc.