All files return 404 when reading them

Ahoy.

We've recently upgraded to CMS 12, and now, all our media files are returning 404 to visitors. 

• When all file paths, blob IDs etc seem correct. They point to the correct files on disk and match records in the database.
• Uploading new files map them to the correct content type, and puts files correctly on disk where I expect it to. Even thumbnails are generated.
• All files in question have Read access for Everyone
• When I open an image in the image editor, the image shows up - so there's obviously ignition somewhere in there.
• They return 404 both for public URLs and the in-edit-mode-URLs.
• We have a single FileBlobProvider, pointing to a folder on disk - so nothing very complicated here.

Any pointers?