Thank God. That only took 2 years. Revisited the broken image links in my Moodle installation and found this gem in the forums.
I had the same problem on my installation. Try going into Configuration > Variables > and set slasharguments to file.php?file=/pic.jpg That fixed the problem immediately in my installation. It’s covered in the uploading FAQ but I didn’t notice the “no input file” message linked to the discussion.
Blogging it here with some keywords in the title for other folks having the same problems.