I have never experienced a loss. If the anemone is healthy to begin with, it should be able to handle the stress. I'm not saying that this persons anemones are unhealthy. I do believe something is causing stress in the tank. I agree with you when you say some things defined as stress are optimum conditions for asexual reproduction. There is no doubt in my mind, that if I went and made some changes to my tank today to cause some stress, I'd double the population of anemones in my tank. I personally would rather have a few large anemones in one tank than a bunch of little ones. Sure they are nice to sell or trade to others, but it is a real pain for me to get them out of the tank.
In my experience it has been mostly equipment failure or water parameters, or transfer from one tank to another. Some have been temperature related, where a heater has malfunctioned. New bulbs or a large water change can also make an anemone split. I have 3 tanks with anemones. When something goes wrong in one tank, they all split. It doesn't always have to be a massive change.