I think this is an urban legend. The "Church properties" didn't belong to the priest in the first place, nor do they now.
I agree, however, there was the issue of benefices.
Actually, simony-—the sin of buying and selling ecclesiastical preferments, benefices etc, and nepotism were rampant among the clergy during the Middle Ages. So were other corrupt practices including the sale of papal indulgences which lead to the Reformation.