Playing devil's advocate: "crystalline" in bulk is different from "a crystal". I think the idea is that individual crystals are "alive" in that sense, and the bulk is maybe a colonial organism. Maybe quartz crystals forming in a chunk of what will soon be granite are only "alive" in the brief period where they are still growing. When the rock solidifies, the crystal "starves" and "dies", leaving only a corpse. Melting and refreezing granite would basically be composting, using formerly alive material to foster new life.

On a similar note, a dead human is "compositionally identical" to a living one, at least for a little while, so I think that's entirely a red herring. :)