After that, they crossed the Arnon River gorge and camped in the Moabite desert bordering Amorite territory. The Arnon was the border between the Moabites and the Amorites.
After we went through Ammon, the LORD told us: Israel, pack up your possessions, take down your tents, and cross the Arnon River gorge. The territory of the Amorite King Sihon of Heshbon lies on the other side of the river, but I now give you his land. So attack and take it!
A little later, the Israelites set out into the desert, going east of Edom and Moab, and camping on the eastern side of the Arnon River gorge. The Arnon is the eastern border of Moab, and since the Israelites didn't cross it, they didn't even set foot in Moab.