First, I think your emphasis is misplaced. Photosynthate provided by zooxanthellae is rich in energy, though lacking in nitrogen and phosphorus. Therefore a majority of energy for zooxanthellate anemones CAN be provided by symbiotic algae - as has been seen in studies on zooxanthellate anemones kept in "starved" and "fed" conditions.
Additionally, it depends on your definition of "food" and whether this includes uptake of dissolved organic matter (DOM) from the water, absorption of organic matter from clownfish, etc. Keeping the discussion to aquariums, does food only mean supplemental direct feeding?
I will agree that clown anemones cannot be kept without ANY nutrients to supplement the photosynthate provided by zooxanthellae. In fact, if denied phosphorous and nitrogen, the zooxanthellae themselves begin to suffer and will eventually starve. But the question is whether or not these need to be ACTIVELY provided in a closed system. There are plenty of examples of anemones growing from small size to quite large without any supplemental feeding beyond that which occurs "passively" in a reef environment. Perhaps you think I'm splitting hairs here, but I think many people feel that if they aren't feeding their anemone a shrimp twice a week, it is going to keel over.
I believe that this helps explain how you can supplementally feed an anemone, and it will grow quickly (all other environmental conditions being kept optimal), but you can stop supplementally feeding it, and it will grow slowly, or stop growing, but rarely will it starve outright - as long as it is kept in a healthy reef environment.
Everything I have said above assumes clown anemones. Certainly there are non-zooxanthellate anemones that are wholly dependent on active food capture. Likewise there are other zooxanthellate anemones that are more reliant on their symbiotic algae than clown anemones - including fire anemones that have almost lost the ability to actively capture prey and whose strong sting is actually a protective mechanism. There are numerous anemone-like creatures (zooanthids, corallimorphs) that obtain the majority of their energy via photosynthate and passive nutritient uptake. I don't think anyone would argue that Ricordea need to capture sea critters in order to grow and thrive - though they will still do so if given the chance.
By the way thanks for the discussion - I enjoy it