I recommend that those who find it so hard to believe: join the dino thread in the chemistry forum. Dinoflagellates are not algae. They create an environment that is toxic to algae. There's no copper, but they do create poisons that kill snails, crabs and fish.
If a scrubber is working at all - dinos can take over - if a chemical is added that rapidly reduces nutrients below where algae needs to survive and dinos can thrive. Please read my full description above and visit the dino thread if you want to recommend other treatments.
If you've never dealt with them, I would advise against jumping to easy remedies prematurely - it's not very kind to those that are on the verge of leaving the hobby because of them.
I personally think a supercharged ATS with a lot of food is one of the answers - but that doesn't preclude an ATS dying and dinos taking over if other chemicals are added.