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Sometimes they suck up a different item. I've found arrows and rotten flesh in there before. Try giving it an open (misc) inventory slot and see if it spits out something that isn't cobble stone.
Nah, you'd just need to unlock rubber trees and feed a huge tree farm or 10 into a few Fluid Transposers. I plan on doing just this in order to automate soul sand/quartz for an ME system.