In my case, it was a new installation. Making the changes as suggested above solved it immediately. As this is in the hosting provider’s support knowledgebase, it is clearly something which they have had occur on a regular basis. I only came across it after having gone through all the configuation settings, as well as searching these fora. Then I figured the hosting provider’s clients might have had this happen before.
Upload path does not exist under Media Settings for site within mutli-site setup. At the top level configuration file, it was correctly set for the root uploads folder, and folder permissions were correct (7,7,7). It just didn’t work until I made the suggested changes as per the above link.