Ok, I see where the "actually 2000" misconception would come from. A mile is 2000 steps, and "mile" comes from "mille".

But "mille" means 1000. Specifically, it was the distance covered by 1000 paces from a marching Roman soldier. It's more consistent to measure paces than steps in the face of left/right asymmetries, so it's the unit implied when you just say you're marching 1000.