Depending on the particularly chemistry, Li-Ion can be safe:
So are they comparing to the best of Li-Ion or the worst? (e.g., the cells Tesla use in their pack are "unsafe", but are made safer by placing them within a fire-resistant casing.)
Lithium Manganese is about the best balance of safety and cost we have right now. (That's what is in the Leaf battery pack and the 18650 cells in your second video.)
It simply smolders for a short period before self extinguishing.
That's why, if you use an eCig mod you're pretty much asking for it if you don't use name brand (Panasonic, Efest, etc.) LiMn batteries. I don't know about you, but I don't want a potentially explosive battery inches from my face, while inhaling *and* drawing 1C from said cell.
Sent from my Tablet