A conditioning relaxer can actually condition the hair as it relaxes. It can be recommended for hair that has been previously relaxed with a no lye relaxer. You are right; just because someone is a hairdresser does not mean by default that that person will do the right thing and know what he/she is doing.
I learned about conditioning relaxers in Shamboosie's book, and he talks about no lye relaxers and conditioning relaxers in detail. I don't know if you found this board when many of us discovered this book. There were a few threads discussing this book, so you might want to check them out. Many of us purchased the book and found that it was very helpful and had some real nuggets of wisdom. We didn't all agree that EVERYTHING he said applied to all of us. For example, he highly recommends Nexxus Humectress moisturizing conditioner. Some of the women here absolutely love Humectress, while others absolutely hate this conditioner. Many of us downright disagreed with some of his recommendations; I remember many of us took issue with his assurance that one can use a curling iron frequently and maintain hair health.
Overall, this particular hairdresser seemed to be very knowledgable about hair care and relaxers. So, in my opinion, he had a pretty stable basis of knowledge for what he was saying. Now, this doesn't mean that everyone needs to go out and apply a conditioning relaxer over their hair. It was simply a recommendation by him as a way of treating hair previously relaxed with no lye relaxers, which over time cause dryness and breakage.