Is it really a grey area? Surely it's just plain old copyright infringement?

If facebook shuts down it doesn't mean all multimedia content that was ever hosted there suddenly gets dumped into the public domain. At most you gave the company that run the site an irrevocable, international license to that content (depending on their TOS), it doesn't apply to everyone else and it didn't get put into the public domain or under some other open source license.

Nintendo is sending all users their post history so they can personally archive it if they wish. If anyone else archives it, it's just copyright infringement...

Personally, I respect the work that the Internet Archive and other archivers do, so this is definitely not a hill I'm willing to die on.