Crank, you are correct on a couple of points.
Yes, you can carve a straight ski. To do so you need to make it bend and that took a lot of technique to do correctly. If you look at some old pictures of racers you can see them carving by bending the ski. Modern skis took the sidecut from snowboards and we found that the ski now has a natural carving arc that can be enhanced by proper technique. (I hate to admit it, snowboarders gave us something good.
Yes, the skiier is far back and is, as you say, sliding/squishing the tails of the skis around. (I like your squishing description.) If placed on new equipment, he will do the same thing because those are the movement patterns he has ingrained in his mind and body.
And you are absolutely correct that you work from the bottom up to learn how to ski. You also do the same thing when tweaking a skiier's form. If you notice, my suggested exercises are working from the ground up. Get the stance right, then work on the feet and ski movement. Upper body, hands, etc. are icing on the cake.