I did keep an atlantic anemone for several months before switching to RO water, and a few other inverts. But the algae gradually began to increase, eventually to an alarming level, and then all my inverts, including a sebae that I traded the other anemone for, began to die off. The anemone just sort of melted. I lost a huge amount of critters in a few weeks time (not any fish though). I dubbed that time "the great die off" My theory is that all the metals etc in the unfiltered water finally reached a critical level in the rock & sand. My LFS gave me about 50 gallons of RO water, I began to use it faithfully from then on, and a few months later no algae, and no problems with inverts. That was 5 years ago (this Sept), and I still have the same sebae that I got a month or so after switching to RO water.
hwynan, you are one of the lucky ones with good water, good for you, I wish I were so lucky. Also agree that the 'nem very well may be sick or injured from the outset, no matter what the water is like. However I still think it is unlikely that many corals or anemones can thrive in unfiltered water, in most places. Also there are countless other possible husbandry issues that are not being addressed here that could be the culprit.