harmon.ie does not share credentials with MS Office applications when opening documents. The office applications authenticate against SharePoint separately. When user clicks on a document - harmon.ie determines appropriate application based on the document extension and then launches the associated desktop application by passing it the URL to the document. Running the application from command line and passing it the direct URL of the SharePoint document closely approximates the behavior of opening the document via harmon.ie.
Please check to see if running MS Office application, such as word or excel, from command line and providing the URL to the SharePoint document would require user to enter their password (sample command format is below - in this environment harmon.ie is installed in Outlook 2010 and opens a Word document from SharePoint URL from our test site)
"C:\Program Files\Microsoft Office\Office14\WINWORD.EXE" "http://ravenwood-corp.com/sandbox/Shared Documents/ER.doc
Check under Control Panel -> User Accounts and Family Safety -> Credential Manager, select Windows Credentials tab and delete any entries that have the same URL as the SharePoint site you are seeing the issue opening documents from.
You may also double check whether the SharePoint URL is added to Trusted Sites or Local Intranet in the Internet Explorer under Tools -> Options -> Security - if not, you can try adding the site URL to Local Intranet or Trusted Sites zones.
