I found your thread, while doing forum housekeeping.

In one sense, non-chemical pools are an illusion, because even water is a chemical -- dihydrogen oxide is a perfectly legitimate name for water.

But there is a slowly growing trend, mostly in Europe, of "natural pools". Essentially, most of these utilize a managed 'swamp' to purify the pool water the same way a real swamp would. Some of the pools are very beautiful, if probably very expensive. But I've posted a picture gallery here:
http://www.poolforum.com/pf2/showthread.php?14427

There are links in the post to two reputable companies building such pools. One of those companies has representatives in the US, so you can contact them if you like.