I love that "above some critical threshold" is listed like a mysterious or complex thing. It's the angle of repose, the angle that a material naturally sits at when you let it fall from a height and pile up. It might be, if things are very complicated, the angle of repose + cohesion, but then you're back at water-based theories again since water is the easiest way to remove cohesion and trigger failure.
I also really like that the experimenters managed to recreate a sand flow in their lab. Of course they did. The field of prior research involving laboratory sand flows is immense, especially if you start including the ones with tiny glass beads of carefully varied diameters instead of sand. The only problem is thioxtropy -- landslides are renowned for having material that exhibit viscosity inversely proportional to velocity -- which is not easily replicable in small-scale lab settings.
I'm not sure if this is a, "Physicists discover what geologists already knew" moment, or a "Journalists are puzzled by the mundane mysteries of science," or what, exactly, but if you want to learn more about landslides on Mars, check out geotechnical journals starting with Lucchitta 1978 (Bulletin of the Geological Society of America, v89, pg 1601) and work your way forward. As the lunar and Martian landslides discredited an entire set of excess mobility theories, they're very well described and discussed.