Not a fear of death on a human's conscious level. It's a reaction to stimuli. Other plants do it as well. When you cut a tree in the forest the trees around it respond on a chemical basis. The point is, that's Life. We are all just tiny parts of the same Life. Humans are neither above or below. We're gifted (a word used loosely) with consciousness of our consciousness.
Studies have repeatedly shown us that plants will muster chemical reactions to all sorts of threats and other environmental changes. And that chemical transfers between plants communicate these changes and dangers.
I digress, I find it hard to swallow all of their sanctity of life blabber so long as all forms are not included. Why should anyone be considered more valuable than anything else; anything, tree, fish, insect, plant, single-celled organism? Each has it's own essential purpose. When ours seems only to be the manifestation, or personification, of the Consciousness. That's what humans seem to be, that's the answer to the age old philosophical question, "Why are we here?" To be the vessel in which Consciousness can be conscious of itself. Otherwise, we seem pretty worthless. We had potential, sure, but instead of nurturing Consciousness, we decided to value ego.
Now that I think of it, that fly, whose larvae help to decompose dead organic material, has more value to Earth than we do as humans. (Evidenced by what we've managed to accomplish for Her in our glorious history of existence.)