It is true. They can trace the genetic lineage. The original plant isn't totally inedible, it's just less nutritious and harder to process. The same is true with wild grains in the Middle East. precursors of domesticated crops like wheat and barley were cultivated from wild grasses which produced less, had less nutrition and took more effort to process into flour.
It's wrong to say they were useless like OP suggests. They were very useful. It was a crop you could reliably grow and come back to harvest.
It also stored very well. The breeding was only to make it more useful. It was always useful.
Much of the breeding was just selection. The crops you would pick and store would be larger. So we it came to plant your were using the biggest largest variety every year. A few generations of this would produce notable results. Then even finer and more deliberate selection would be done.