But they have zero proof about being real. Using the API was proof. I can make any tweet from any user, take screenshot and you can’t prove it was not real.
You're reading news sources where you think it's a serious threat that the journalists might fake a tweet? Why would you care about what any site with that low of a reputation has to say?
It may not be an issue with established, reputable news sources you're already familiar with, but it certainly could be with every other website out there.
It does not provide any additional value, since that can be faked as easily as the screenshot. Any validation requires something from Twitter end-point, that they check and verify publicly that it actually existed at that time… but that does not work since we are going against removals made by Twitter in the first hand.