I have the map " Training grounds " setup , and in the middle of it there's a black square, which looks like a giant pit or something. (if it were a space station, I'd say it was space). This square is surrounded by dashed red lines, indicating impassable terrain.

One of my figures is massive. Can he rest on this space? If this were normal impassable terrain, the answer would be clear (yes). However, my opponent argues that the black void space has the same status as any other black 'off map' area, and that the only reason the dashed red lines are there is to indicate that line of sight is possible across this area.

In other words, the elevator on core tile 19A.

The black spaces are not surrounded by walls, so they are simply impassable spaces. The black used in the graphics is just graphics - and there is even a grid that is not black (which seems to be visible also in the playing mat version) differentiating the elevator shaft from a wall. A massive or mobile figure can enter the spaces, line of sight can be drawn through them, and you can count spaces through them.

(Otherwise, why the dotted line? You cannot draw line of sight or count spaces through walls. Putting impassable edges next to a wall doesn't allow you to draw line of sight or count spaces through walls.)

Yeah, it's the freight elevator from the Death Star hangar/docking bay, not a giant square wall. Most of the art on the tiles corresponds to terrain seen in the movies. It's fun to look at the tiles and figure out what movie scene they were depicted in.