I don't know how hattie does it , but I've grown lots of tomatoes by pulling "suckers" and then sticking them in the ground. I always put a bucket with a few holes in the bottom beside the "suckers" for about a week and keep it full of water to keep it from drying out until they have started a root system. I've had "suckers" produce more and bigger tomatoes than the plant I pulled them from. 

We had a guy who had a cube right next to the south facing window. He had the same tomato plant that had been growing for three years when I met him. THREE YEARS! And he got lovely tomatoes off of it! He had some cuttings started because the plant was just way out of control (he had strings holding it up to the ceiling). Tomatoes root easily (that's why we bury the stem, more roots equals stronger plants, but I know you know that, Steve!).