Another option might be to deal with the table only and bypass the header row when looking for the visible rows after filtering.
Code:
Ass_Num = Intersect(acrow, tblColumns("Asset" & Chr(10) & "Number").Range)
Sheets("backup").Select
With ActiveSheet.ListObjects("Customers")
.Range.AutoFilter Field:=6, Criteria1:=Ass_Num
Set fRng = .ListColumns(1).DataBodyRange.Cells.SpecialCells(xlCellTypeVisible)
fRng.Cells(1).Select
'.Range.AutoFilter
End With