FWIW, this doesn't work on a Motorola Droid 4.
This phone has "hard" keys for menu/home/back/search and pressing the menu key does nothing while viewing an attached image full-screen. Likewise, a long-press does nothing, attempting to zoom in/out on the image does nothing and swiping does nothing. C'mon Google!!
On a MMS message with multiple images attached, I WAS able to long-press on the inline, smaller image, but it seemed that I could only forward them to another hangout.
Luckily, the old Text/MMS app still works and contains all the same messages, so I was able to use it to save the attachments and relay them as needed.