From what I have read of the posts so far the first mistake was to set autobrake. If the pilot reads in the tech log that the aircraft had a known history of braking problems you wouldn't set autobrake on the approach, surely? Use reverse thrust and then gingerly apply the brakes once the aircraft had slowed significantly with your hand firmly on the nose wheel steering to compensate for any swerve.
It is not unusual with a big aircraft like the A330 to have to apply quite a lot of extra thrust to keep it moving when you leave the runway. Therefore the pilots may have not noticed. Bear in mind when doing a 180 on a runway you end up sitting well over the edge of the runway as you turn. So a sharp left turn on to a taxiway would require to be sitting over the right edge of the taxiway as you turned. If the pilot wasn't in the correct position he may have cut the corner and gone off the paved surface.
The engineers would have then noticed the damage afterwards and may have been advised by management to keep it quiet. The pilots don't do an external check after shutdown. Once the aircraft is shutdown you pick up your bags and leave.