The are where I live is 100 km from any rivers/streams or any moving water of any kind. There are only a large number of shallow, stagnant alkali sloughs containing water and they are absolutely littered with goose droppings. Wouldn't drinking this make them sick?
Historic water sources in the US are often unmarked or no longer exist. In many parts of the US (including the plains), overuse of groundwater has dramatically lowered the water table. This has led to the drying up of many streams and ponds that would have been used by natives. Damming of rivers for irrigation has contributed significantly to this as well. There are still many water sources that people no longer use and are not marked on modern maps. This especially true in the American deserts, where you're never more than 45km from at least one historic water source. Natives would have been able to cross even the driest American deserts without needing to carry more than a day's worth of water. This is still true in many areas today.
There's a cultural component as well. Plains tribes would have known exactly where to find water in their environment through shared knowledge. When you need daily water, you're unlikely to stray far enough from a good water source that it becomes a problem.