The draw order for a typical 2D isometric scene is determined by the Y-coordinate of the objects - i.e. objects are drawn top to bottom, so the objects "closer" to the camera are drawn on top (in front) of objects that are "further" away.
A vehicle is a long object and can cover multiple tiles across the Y-axis at certain angles. When you have such an object, it makes sense to consider its coordinates to originate from the centre of the object. If the draw order of the vehicle is determined by its centre Y-coordinate, however, there can be cases like this where an object that is just below the centre of the vehicle, yet supposed to be underneath it, is drawn over top.
That is my guess, at least. It would explain why the grass in the video only clips through the lower portions of the vehicle. It would be quite an easy fix, too: Just pass the renderer the Y-coordinate of the vehicle's lowest point, rather than the centre.