I was going to mention BLM land. I thought the same rule applied, but I wasn't certain. I have only stayed at developed campsites on BLM land. Stayed at a very nice on in Divide MT. Right next to the Big Hole river. Fresh, cool drinking water. Clean vault toiletes. And the host gave us free firewood. All for $6 for the site.
Fishing access places are other good spots. I stayed at a couple out west.