I know for a fact that paintballs are water soluble and easily wash off
Inquiring minds want to know: Have you ever tried dousing a cushion-- or anything else absorbent-- with any kind of paint, water-based or otherwise? If there exists a Mrs incrediBILL, I am going to guess no. At least not more than once.
I don't care how non-toxic, water-based or outright edible the stuff is: You are not going to get it out. Most things you eat are water-based, but just try cleaning a wine or coffee stain :)