The same customer that was trying to upload the problematic mp4 video, also ran into “WordPress: Unexpected response from the server. The file may have been uploaded successfully. Check in the Media Library or reload the page”.
They were trying to upload mp4 files that were up to 400 megs in size. WordPress was configured to accept files as big as 800 megs, but every upload ended with this unhelpful message.
Come to find out, CloudFlare puts a 100meg upload limit on all free accounts. We love CloudFlare and we completely agree that they can put any limit they want on their free accounts, but, wow, that was certainly an unexpected source of the problem. You can still use cloudflare’s DNS, but you have to turn off proxying if you want to upload files that are larger than 100 megs.