Well I wallowed around in this one long enough. It seems that just adding DoEvents after the Documents.Add method eliminates the anomaly.

Sub Demo_LostSelection_AnomolyI()
    Dim oRng As Range
    Dim oDocTmp As Document
    ActiveDocument.Range.Text = "One two three"
    ActiveDocument.Words(1).Select
    Set oDocTmp = Documents.Add
    DoEvents
    oDocTmp.Close wdDoNotSaveChanges
    'Notice after the procedure runs that the selection is reset to the start of the page.
    lbl_Exit:
    Exit Sub
End Sub