Ok, it seems the images are uploading properly, so it is not a permissions issue. It seems the images size variations are not being created. I wonder if this is related to a bug the (well, not really a bug) that affects a very small number of users. If the webhost has Imagick installed (which is good since it is more efficient) but an old version which does not have a function that is being used the images will not be created. This, however, always throws a PHP error.
You know I think WP_DEBUG also has to be enabled to see the image process log. I added it (and forgot) because users would enabled the debug and forget then would ask how they could disable the process log. Here’s a link that explains how to turn it on: