Recreational Water Illness

The CDC has printable cards for Kids about the illnesses they fight and research and whatnot. My favorite that I've looked at so far is Recreational Water Illness.

On this card we learn that:

Recreational water illnesses (RWIs) are caused by swimming in water contaminated with germs like "crypto," short for Cryptosporidium...RWIs that cause diarrhea are spread by accidentally swallowing swimming water that has been contaminated with feces (poop).

Heh, they said poop. And who's been letting Superman's dog swim in people water?

The card also gives three ways we can stop these RWIs:

PLEASE don't swim when you have diarrhea.
PLEASE don't swallow the pool or lake water.
PLEASE wash your hands with soap and water after using the toilet and before you get back into the water.

PLEASE don't poop in the water you swim in, only in the water in the toilet. I guess it is okay to poop in river water, since they don't say that it isn't.
Would it be okay to go swimming if I have diarrhea, but wash my hands before I go in?