There are different classifications for different types of lands. For example, Federal law applies to monuments, parks, military bases, federal buildings, etc. Local criminal law usually applies to National forests, BLM lands, Grasslands. Hence the Park Service runs rescues in parks, County Sheriff's run rescues in National forest land. I am not sure what the distinction is, but there is one.
That's why the Park Service shuts down parks, but you can still hike in a Forest. i would imagine that BLM and Forest Service rivers will be launchable, Park Service will not. If you want to run Cataract, launch upstream from Mineral (Spring I think) Canyon and see if you can float through.
You should be able to run Westwater, Deso & the San Juan, but the Yampa, the Grand, Big Bend, Gunnison in the park, and Cat launching at mineral or Potash will get your ass arrested, charged and all your shit confiscated. You also have to appear in a federal Court in the state it occurred in, like Salt lake or Denver. A serious pain in the ass if you're an out of state boater.