Not sure on the pat but the wrangler and liberty have an antenna in the way on the passanger side. Back in like 04 you could write Jeep and they would send you a trail rated badge for free. Not sure if they still do. You could always take it down a trail and lay it into a rock on the passanger side and use the resulting scrape and dent as your trail rated badge.
I heard it explained once that Jeep views the trail rated badge as a medal. Military wears the personal medals on the left, (I think the navy is on the right, someone will correct me I'm sure) so the jeep wears its medals on the left.