Actually, this makes perfect sense. The Amish avoid any "modern" device that creates a dependence/connection with the outside world. Electricity is "hard wired" in on power lines, and so is shunned. Bottled propane for stoves is allowed. Paintball guns, via the propane example, would be permitted...they run off of CO2 cartridges, right?
However laudable the Amish contention to shun material things, though, it sounds like the rules can be parsed for the right reasons...I have heard that cordless power tools, run on DC batteries, are permitted by clergy to be used in the famous Amish furniture!