Why are the Ammonites excluded instead of the Midianites in Nehemiah 13?

> Now Balak son of Zippor saw all that Israel had done to the Amorites, and Moab was terrified because there were so many people. Indeed, Moab was filled with dread because of the Israelites. > > The **Moabites** said to the elders of **Midian**, “This horde is going to lick up everything around us, as an ox licks up the grass of the field.” > > So Balak son of Zippor, who was king of Moab at that time, sent messengers to summon Balaam son of Beor, who was at Pethor, near the Euphrates River, in his native land. *(Numbers 22:2-5a, NIV)*
> On that day the Book of Moses was read aloud in the hearing of the people and there it was found written that no **Ammonite** or **Moabite** should ever be admitted into the assembly of God, because they had not met the Israelites with food and water but had hired Balaam to call a curse down on them. (Our God, however, turned the curse into a blessing.) When the people heard this law, they excluded from Israel all who were of foreign descent. *(Nehemiah 13:1-3, NIV)* Why did the Israelites at the time of Nehemiah exclude the Ammonites and Moabites from entering the Temple, when it was originally the Midianites and Moabites who hired Balaam?