I've heard the bleach theory too.
The amount you have to put in the bath is so small that it resembles chlorinated water from a swimming pool.
I think that it how they originally found out it worked, because they noticed the eczema on children was improving when were swimming in chlorinated swimming pools.
My son had terrible eczema all over his body. I had to use celestone until it cleared up. Once it was totally gone I could stop using it and now I just have to make sure his skin stays moisturised by using QV bath oil and sorbolene everyday. He occasionally has a flare up, but it is usually easily treated with Dermaid which is available over the counter I didn't end up having to resort to the bleach baths, but would try it if nothing else worked