Ok, so I tried a couple more things. I installed mod_pagespeed on my dev server, and saw no savings, even with their beta version. This is exactly what they use for the online tests (or should be), so that was a bit surprising.
Last test was to upload to my test server online here: https://test.shanebishop.net/2014/10/23/testing-unsquishable-jpg/
You can run that through pagespeed yourself to see the results, but they surprised me, because it showed no savings available on the images, and I then re-downloaded that image just to make sure that it was the same size as the original I grabbed from your link.
This leaves us with 2 possibilities:
1. You have a plugin that is slipping data into the images when they are viewed, but not when they are downloaded.
2. Google has a bug in their pagespeed scanner that is somehow being triggered by your page(s) specifically.
Either way, the images ARE fully optimized, but it is a puzzle as to what is causing the discrepancy, unless you have a plugin that is doing something sneaky with images. Perhaps a list of your active plugins would be useful to try and rule that out.