They got clearance and then obviously didn't bother to look outside, which is a dereliction of the basic responsibility of operating any vehicle on an airport surface. Clear left, clear right, then cross the hold short line.
(See my other comment below if you're tempted to say something about visibility.)
They could not see, because delta crosses in diagonal to the runway, such that the plane comes from behind (and the right side) so the driver has no chance to see. The truck was moving fast which is ok, because you want to clear the runway as fast as possible.
It doesn't matter what the orientation of the taxiway is. If you can't see when you're stopped straight on the taxiway centerline, you stop at an angle instead.
There is never an excuse for not visually clearing a runway before entering it.
(See my other comment below if you're tempted to say something about visibility.)