I agree that there are conflicting sources of information on this - and I apologise if our documentation is inaccurate, I’ll look into that as soon as I can. We intend to follow the Google specification on this.
I can tell you that when I attempt to fetch the image directly through our crawler, it reports that the robots.txt file is blocking access, so I would suggest either removing the disallow on the parent folder, or setting a directive before the all robots directive that grants Twitterbot access.