OK, you cannot use that method when the table has merged cells. The following however will work with that table whichever header it is in (It is in the first page header in your sample)
If you want to select which header, then you will need to replace the line
oTable.Cell(1, 2).Shading.BackgroundPatternColor = 11382784
with
oTable.Range.Cells(3).Shading.BackgroundPatternColor = 11382784
Sub Macro1()
Dim oSection As Section
Dim oHeader As HeaderFooter
Dim oTable As Table
For Each oSection In ActiveDocument.Sections
For Each oHeader In oSection.Headers
If oHeader.Exists Then
If oHeader.Range.Tables.Count > 0 Then
Set oTable = oHeader.Range.Tables(1)
If oHeader.Range.Tables.Count > 0 Then
Set oTable = oHeader.Range.Tables(1)
oTable.Range.Cells(3).Shading.BackgroundPatternColor = 11382784
End If
End If
End If
Next oHeader
Next oSection
lbl_Exit:
Set oSection = Nothing
Set oHeader = Nothing
Set oTable = Nothing
Exit Sub
End Sub