I would say the crucial thing is actually making a falsifiable prediction, not having a scientific grounding. There are also many "just so" stories that make sense at face value but are not really falsifiable (e.g. Evo psych is full of them). I think the theory here does make some falsifiable predictions, which is great, so guess we will see. But I'm not holding my breath.
Good point. I don't understand their claims, and I don't have a horse in this race, but I'm really interested to understand the mechanism in more detail if it turns out to be correct because it sounds so bizarre.