When I've talked to the backcountry office at Theodore Roosevelt, no one could tell me exactly why you can't drink the water in the park. This picture might tell the story.
There isn't much water, though there are some creeks and springs. It's very alkaline. It gets trampled a lot by the bison and other wildlife. And, well, it just looks gross.
This stretch of Paddock Creek is actually the best water we saw while there. In an emergency, this would have been as good as it gets.