One of the recycling steps is dissolving the lithium in water. So they might just as well take a burning battery and just chuck it into the shredder, and then mix the burning slurry with water.

Contrary to the popular belief, lithium batteries do NOT contain enough oxygen to just keep self-burning. Most of the lithium-ion pyrotechnics is just from good old atmospheric oxygen, which oxidizes the organic electrolyte.

What lithium-ion batteries have is the ignition source that basically keeps going on and on. So once you extinguish the burning electrolyte, it just keeps reigniting.