Aiptasia also release planula while being disturbed, which is why manual removal of aiptasia is not recommended unless you can do it without disturbing the aiptasia. Hence the comment "your tank is infected". Manual removal of the anemone would have triggered a release of planula. So, while terminology is incorrect, the basic gist of the comment is correct.
Also, fungi aren't the only producers of spores. Some bacteria do as well. I see where you were going with the facepalm but it was unwarranted and kinda douchy. You could have just said "they release planula, not spores, which are the larval stage of aiptasia. These resemble ciliated protozoans and are free-swimming in water. They grow into an adult aiptasia when they encounter a hard surface and attach."
I would have tried berghia nudibranchs, personally. They don't care about size of the anemone and you could have passed them on to someone else with an aiptasia problem once yours cleared. They are obligate feeders on aiptasia so no worries about them snubbing aiptasia (like peps might) and they will leave your corals alone. In a little tank they would be much easier to recollect and pay forward.