Update: Jan. 23
The New York Times reports, in a Business sections story by Kashmir Hill, that Twitter has sent a cease-and-desist to a company called Clearview not to scrape images from Twitter for a facial recognition database. That is obviously because the company wants to deploy the images commercially for security customers. But theoretically that could mean that a social media company or newspaper would object to people keeping images on their hard-drives even for private use (never published online). It still might be picked up in the Cloud if someone developed the tools to do this to go after individual users. You could imagine combining this idea with the Case Act (not yet passed) and the Copyright Office, if you wanted to.