So update the documents?
I mean, you're clearly not describing a high documentation culture, you're describing a culture that underinvests in intra-organizational communication.
I run a high documentation, low meeting culture by necessity (we operate in five time zones around world). Meetings vs docs is remarkably similar to the decision between paying for office space vs paying for occasional team retreats. If you run a fully remote company retreats are almost always a better use of your money than leasing office space. But you still need to pay for something.
Similarly with meetings vs. process documentation. If you're heavily remote and spread out I'd say you should cut down on meetings and being high documentation is the better choice. But again you still need to "pay" for something - you save time on meetings but you need to reinvest at least part of that time into writing documents.
Another bonus of documents is that they scale better than meetings. McDonald's doesn't deliver the same big Mac in every corner of the world by holding a lot of meetings. They have a book that goes out to all of their thousands of franchisees. When they want to add another thousand franchisees, they print more books.
If the documents are out of date my answer to my team is always "update them!" Anywhere that we're writing documents there are revision and discussion features so it's not like you can irrevocably screw something up, just improve it and let us know what you did. I do struggle with getting people to actually do it though.