Borealis,
As BOAC says, I don't think any of the newspaper reports, or quotes from DFW spokesman, are referring to the crews making inaccurate loadsheet entries. The alleged under reporting of the MTOW would be in the figures provided to Eurocontrol in the annual return submitted by the operator - according to the quote attributed to the DFW spokesman, a MTOW of only 66,990 has been reported to Eurocontrol but the aircraft have been operated at higher "approved" MTOW (under a flexible MTOW regime). The issue is that, if a flexible MTOW regime is being used, the operator is required to report (and will be charged for every sector) at the highest allowable MTOW and cannot just pick and choose.
As per a previous post, there could be a secondary issue if the Noise Certificate for the aircraft is also only stating an approved MTOW of 66,990 (which seems to be confirmed by the data published on the IAA website) and the aircraft is operated at a higher MTOW. As far as I am aware, the Noise Certificate forms part of the aircraft's certification so the MTOW stated should not be exceeded.