Thanks for the help and clarification on this. That solved the problem. So, when the 'Data Store' asks for the 'Publisher folder path', it wants the file path the Map Document(.mxd) is using - which will always be a Windows path because you can only author a Map Document on Windows. When the 'Data Store' asks for the 'Server folder path', it wants the path that the Server needs to use to read the data. This could be Windows or Linux.
Sorry to say that the documentation on registering a folder is not very clear. The word 'Publisher' is a poor choice. Publisher of what? Now, I know it means 'Service' publisher. But I was thinking it meant 'data' publisher (which would have been my Linux file share).