Short Approach?
A possible explanation (not excuse)...
I will guess that they were not a GPS-equipped jet, and that their Nav Display (called the MAP) was off a bit. The non-GPS jets update FMS position (MAP position) based on IRS inputs and DME inputs. That can be off a mile or so after 9 hours of flying. The jets with GPS do not have that problem, and typically keep the FMS position very accurate...often within .2nm or less.
Localizer signal quality can be erratic at some places (Brussels is a known location), and it is preferred to stay in HDG SEL or LNAV (and look at the MAP instead of raw data) so that the autopilot is not chasing what looks like a windshield wiper. Still, one look at the raw data would clue the crew that they have not overshot the localizer.
My guess is that you got their attention by questioning them, and that they reported the situation internally and anonomously so as to spread the word.