The goal of a crash test is not to keep the car intact, it is to keep the driver intact. On "keep the car intact", today's cars do way more badly than those of the 1950's.
Nice video, deserves my upvote, but I am going to call it just anecdata ;-), so that I can add some partial counterarguments.
The video is a commercial, so they will have chosen an impact angle and speed that makes the newer car look best). For example, you can see that the newer car is heavier than the old one from the video; its front wheels still move forward when the wheels of the old one already go back. Because of that, the new car has a much longer braking distance than the old one. Things would have looked relatively better for the old car if they had chosen a collision with a concrete wall.
If its crumple zone is bad or absent, chances are that the older car would have survived way better in a frontal collision, where the beam carrying the engine would be elastically compressed without deforming permanently.
That would be just the car, though; those old cars could be lethal at incredibly low speeds, for example by impaling them on their non-collapsible steering column.
Great video. Pretty clear that both occupant and vehicle fared worse in the 1950s. (Although after a serious collision I doubt many people care much how the car looks.)
You also have to factor in a lot cars in those days didn't have, and weren't required to have seat belts. This safety feature alone has saved thousands of lives regardless of how safe the car is.
Another interesting crash test is the Smart car. Youtube some videos of it. Due to its small size it hardly has any deformation zones and has to be built as a hard cage. It looks quite intact after a crash but i don't think the passengers inside would be.
I believe one of the tests is crashing into a wall that yields very little, so the tungsten dumptruck would fare poorly, exciting as it would be to drive.
The wall at left in that video is, at most, four dump trucks in volume and perhaps constructed of reinforced concrete (density ~2,500 kg/m^3)?
A single solid tungsten dump truck would have almost twice the mass of the wall. Even with a completely inelastic collision, the wall's going to shatter and move. For a 35 mph collision, I think you're right, that wall would ultimately bring the truck to a halt from friction with the ground. At higher speeds, I think the truck might make it through.
Tungsten is quite dense (19,300 kg/m^3). Such a truck would have a mass of >400 metric tons (2 x 3 x 4 m x 19 tons/m^3), or >247 Toyota Tacomas (2013 extended cab, curb weight 3560 lb --> 1618 kg).
The truck would be terrifying to drive, once you got it going. I don't know how you'd turn.
Alas, Youtube is short on tungsten dumptrucks, but this may suffice. In a demonstration, a truck uses its brakes to stop after obliterating a few cars. The truck is driven by a real person.
If you're going to win, you might as well reach the destination without noticing that you've had a collision.