I'm not sure I would say this is 100% true (if it's velvet then yes agree with you), is it advised to treat ick? absolutely. I have QT all my fish for 6-8 weeks with Prazi and copper and currently have 6 of the 14 fish in my tank being tangs- Achilles, Purple, yellow, Mimic, Blue Tang, Chevron to go along with a large Moorish Idol. All have gone thru QT and no tang has been added to my tank in over 3 years. My Achilles was the last one added and has constantly shown signs of ick for 3 years. He is the healthiest fish and definitely runs the show in the tank he's the boss. Ick management has worked for me, I don't advise it nor recommend but it's possible. Other than the blue tang no other fish has ever shown symptoms in the past 3 years. All fish are healthy and thriving. So in a effort to try and beat this after 3 years I decided about 3 months ago to incorporate a large UV and a cleaner wrasse to experiment with the Achilles ick. Not sure what did it but for the first time in 3 years the AT has zero signs of ick. For 2+ years he would get several ick spots and go for a week or so then clean for a few days then back with 15-20 spots and so on. This was non stop for 3 years. The last 6-8 weeks he has not shown any symptoms of ick. I'm positive the cleaner wrasse OR UV had a hand in helping. The cleaner wrasse pays a visit to him few times a day and he goes to town cleaning him, the Uv runs 24/7. It's actually quiet amusing and now the wrasse is the first fish to the large Nori station each day and pigs out with the tangs enjoying Nori and cleaning the fish.
So with that if I could take all my fish out again and treat/ go fallow then yes that's always my first advise but for me ick management was my only real option without tearing down my mixed reef. I have been fortunate in my 20+ years of keeping SW fish to never experience velvet. I keep a QT running full time now and IF you are able to take the fish out and treat I would recommend you do that. Just wanted to share my thought that ick management is possible. Daily I feed 4 sheets of Nori, LRS frozen, Spirulina flakes and NLS pellets all soaked with selcon and vitachem and it's worked for me. Best of luck to your tank.