It is perhaps worth noting that the watermark application mechanism appears to have changed since the update: instead of reloading the Media Library page, it now displays a spinning circle-thing over the thumbnail just before it drops the “Cheatin uh?” error.
Switching to Twenty Sixteen is no good, so it’s probably not theme-related. I have also tried disabling other plugins and that didn’t help either.
All users of the site have the same problem.