for the non-pedologists:
Sandy clay is a textural box on the soil triangle. It’s small and requires the absence of silt. The reason we joke about them not existing is because of the size of the box and how far apart the two grain sizes are. There are very few scenarios where sand and clay would be deposited and not silt.
The chart always looked wonky to me until I saw a version a former coworker had in his cubicle that put sand at the top instead of clay. For some reason the whole thing makes more sense that way to visualize the relationship clay has with silt and sand.
Just rotate the chart that was posted so sand is at the top and see if you see what I mean.