I've had videos taken on my iPhone play upside down on the PC. Apparently, you have to hold your phone with the home button on the right to take an upside right video, even though it plays correctly on the phone. Maybe pictures are the same, and the photographer took an iPhone picture with the button on the left.
Very strange. Poor bloke, his 1st entry and it probably got pinged badly for this. He doesn't say what was used to shoot this but I'm guessing it may have been taken and uploaded with a smart phone or tablet. I will have to check for this in the future if using one of those devices.
This is what happens when a camera records the orientation and embeds it rather than rotating the image itself. Same thing would (should?) happen if you shot upside-down with (most?) dSLRs and uploaded the unedited image. Editing software, for the most part, knows to rotate the image accordingly for viewing and resaving... I'm guessing browsers don't.
So just save a copy somewhere, or do some non destructive editing (e.g. add a blank layer, then save - don't "Save for Web" - a copy as a jpeg at the same quality setting as the original). If you really want it to be identical, pixel-for-pixel, I'd suggest loading the two as layers and setting the top layer to "Difference" - just to make sure.