You should never see feces hanging from a saltwater fish in the same way you see goldfish poop. Usually the current is more than enough to break or disperse it. If the fish is actively moving about, that should also break it. That makes me think its more than just diet, though that can easily be a contributing cause.
That its stringy, and staying together while attached to the clown makes me think internal parasites. Often not serious. A simple change in diet may help the clown beat the bug on its own. They are pretty tough little fishes, if its moving well and eating well i would hold off on medication though I would separate the one not showing any symptoms if possible.
I have one pair of occelaris, a single occelaris, a pair of maroons, and a clarkii. I haven't ever seen that kind of poop on my fish at home, though I do sometimes see it on new arrivals at the LFS where I work. My fish are in a stable system and fed a diet primarily of spirulina flakes, and weekly mysis, krill, whatever else frozen I have managed to fill my freezer with. Point being, primarily algae flakes, so I can hand feed them and they learn not to bite me. A nice varied meal once a week to fill in vitamins and the like. The new arrivals at work are fed a similar mixture though instead of algae flakes they get the hatchery food.
That said, the ability of a parasite to express itself is generally due to stress on the fish. Once the new arrivals have acclimated, and have stayed on the same diet [presumably they didn't show symptoms at the hatchery] with a bit of a frozen super slurry here and there they clear up in no time. Give the fish some time to get used to you and calm down.
If the problem persists but does not worsen, try gradually lowing the Specific Gravity [salt content] of your water to around 1.012~1.015. This makes it easier on the fish to maintain its internal salt levels and gives it a bit more energy to fight the bug. Also lowering the temp to the low 70s can help by slowing the metabolism and encouraging the fish to rest.
If that fails, use the meds they mentioned above. Usually someone will just spit out an answer if they had a similar problem and found an answer that worked for them. I try to stay away from the meds myself because of cost and potentially further stressing the fish. If they are too stressed the meds won't do any good. If the fish seems its might be on its last legs, try some meds. I had never had success with medications before but as a last ditch effort I used API general cure to fight a nasty case of velvet in my freshwater tanks and it worked like a charm. It saved goldfish. Sometimes the meds work wonders.
Garlic helps attract the fish to the food and it seems to help them repair fin damage and the like more quickly. Its not a super cure all but it certainly helps
Spirulina i think contains fatty acids that help with general development and the like but I have done little research into it. I feed it with great success.
Sorry for the long post but the thread seemed a bit off topic.