Sounds like a permissions issue which is rather strange to say the least, because the Alfresco Share app gets the logo image file so I would not have expected file permissions to affect it.
Try loading up Share as a non admin user in your browser with Firebug (or whichever browsers debugging tools you use) switched on and look for the net call to load the logo (the file ia app-logo.png from memory) and see what error you get. If its 403 then its permissions.
