Ammonites Claim Amorite Land?

In Judges 11, when the Ammonites attack Israel, the judge at the time, Jephthah, sends a messenger asking the king of the Ammonites why they are attacking. The king says, "When Israel came up out of Egypt, they took away my land from the Arnon to the Jabbok, all the way to the Jordan. Now give it back peaceably." Jephthah accurately replies in verses 15-27 that Israel took the land of the Amorites after they had attacked Israel for asking to pass through their territory (see Numbers 21:21-26). So why did the Ammonite king consider that his land? The Concordia Self-Study Bible says, "When the Israelites had first approached Canaan, this area was ruled by the Amorite king Sihon, who had taken it from the Moabites. The Ammonites had since become dominant over Moab and now claimed all previous Moabite territory."