Is it obligatory to wash the areas splashed by water used for cleansing (istinja'), which cannot be seen to verify their purity?

If the water that splatters from the bidet during Istinja' (cleansing after relieving oneself) is pure, and if it is from the Istinja' water itself, then if it separates without being altered by impurity, it is not judged to be impure, and the areas it touches do not need to be washed. However, if a person is certain or strongly believes that the splattered Istinja' water was altered or separated before the area was purified, then it is impure, and the areas it touched must be washed.