The Google Docs URL is public whether or not you send it through Facebook. It's only secret until someone guesses the link (Edit: maybe not mathematically in the case of Google Docs, but many other services use 'unlisted' URLs without having a long token to guess) - something they can do without the URL even going through Messenger.
If you're sharing passwords or confidential information via a public URL with no authentication and hoping nobody finds the address, you're asking for trouble. I don't blame Facebook for not doing anything about it.