Alternatively, what if you do have such accounts and don't know the passwords? I keep all my passwords in a password manager, and if I'm crossing a border, I'm probably going to make sure I can't access it until after I'm across.

I'll guessing the right thing to do, if you know about this requirement, is to set up a Facebook account specifically for this purpose, then right before you cross a border, change its password to something easy to remember.