I also wonder whether documents in large companies are booby-trapped, maybe with letter inversion or subtle phrase changes, so that when it’s leaked to the press, they can detect the leaker.
Printers in offices leave some hidden prints on any printed paper. That's how many people got caught, including a serial killer who used a library printer. Whenever one uses company fax machines, these faxes are recorded: some executive in the valley faxed a company report to some hedge fund, she got busted.
All outgoing and incoming mails in the corporate server are stored for some years; that's why large companies use third party for mail services, as these third parties are specialized in auditing, spying, etc.
The other way people exfiltrate is using steganography: convert normal files into images, then exfiltrate these images via USB, cloud, etc.
Maybe, the easiest way is just take pictures of documents with personal phone. That's why air-gapped environments don't let people with personal phones.