That happens because the foreign object, in this case the other player is technically outside your vehicle. He looks just like he's inside, but the cockpit gets drawn in front of him. Same happens for example when you point your rifle at a wall. It might stick through it from 3p perspective, but in 1p it doesn't go through the wall.
Drawing the 1p can be turned off, but then you lose the much more detailed 1p geometries of that weapon/vehicle etc.