Here is the code I wanted to run, to solve the problem I've had to
write a stored procedure which seems to work.
But this has the disadvantage that I need a stored procedure for every
table I want to be able to import into, instead of being able to use a
generic method that matches fields from the csv file to the sql table.

   '''''''''''''''''''''''''
   ''' Create parameters
   ''' and SQL
   '''''''''''''''''''''''''
   For index = 0 To field_count
       Set cmd_params(index) = Nothing
   Next

   For index = LBound(matched_field_indices) To
UBound(matched_field_indices)
       Set param = insert_cmd.CreateParameter( _
           name:="@" & target_fields(index), _
           Direction:=adParamInput, _
           Type:=adVarChar, _
           Size:=8000)
       insert_cmd.Parameters.Append param

       Let sql_fields = sql_fields & "," & target_fields(index)
       Let sql_params = sql_params & "," & param.name

       Set cmd_params(matched_field_indices(index)) = param
   Next
   'Trim leading ,
   Let sql_fields = Mid(sql_fields, 2)
   Let sql_params = Mid(sql_params, 2)

   Let sql = "INSERT INTO " & target_table & " (" & sql_fields & ")
VALUES (" & sql_params & ")"
   Set insert_cmd.ActiveConnection = target_conn
   Let insert_cmd.CommandText = sql
   Let insert_cmd.CommandType = adCmdText

   rs.MoveNext
   While Not rs.EOF
       For index = 0 To field_count
           If Not cmd_params(index) Is Nothing Then
               cmd_params(index) = rs(index).value
           End If
       Next
       insert_cmd.Execute options:=adExecuteNoRecords
       rs.MoveNext
   Wend
   rs.Close