I purchased another Tracy Eichheim spindle, the hearts production spindle seen HERE. On the sheet that came with the spindle it states, "DOGS chew on spindles! One lady came home to find her dog had opened her backpack and totally destroyed her spindle. I have repaired several spindle stems with teeth marks. Be warned!"
So it seems I'm not the only one with unruly spindle-eating pets. Here's a photo of Peaches & Jack the cat where they both look like they're up to no good.