I got the same error, but it seems the message is misleading. I found this article:
http://support.microsoft.com/kb/209953. When I incorporated the DAO.Workspace object and the password in the OpenDatabase arguments from that article into the code you posted, it worked.
Sub UsingDAOWithWord()
Dim docNew As Document
Dim ws As DAO.Workspace
Dim dbNorthwind As DAO.Database
Dim rdShippers As Recordset
Dim intRecords As Integer
Set ws = DBEngine.Workspaces(0)
Set docNew = Documents.Add
Set dbNorthwind = ws.OpenDatabase("C:\Temp\Northwind.accdb", _ False, False, "MS Access;PWD=northwind")
Set rdShippers = dbNorthwind.OpenRecordset(Name:="Shippers")
For intRecords = 0 To rdShippers.RecordCount - 1
docNew.Content.InsertAfter Text:=rdShippers.Fields(1).Value
rdShippers.MoveNext
docNew.Content.InsertParagraphAfter
Next intRecords
rdShippers.Close
dbNorthwind.Close
End Sub
I'm a Word guy, not so much an Access user, so I'm not sure what made OpenDatabase throw that particular error, or how you're supposed to find out about these requirements.