They told you a lie. The biggest breams and often dentex too you find in the shallowest water, when the sea is calm again after a period of rough sea. Go as quiet as possible and be ready to react quickly.
Skaros, the local parrotfish species can be found in many places, the bigger ones are more skittish, however on one of the islands I sawa male parrotfish of approx 50cm, which really is as big as they possibly can get. I didn't shoot it, I let it live so it can have giant offspring. Many nice species are in the shallows, but highly depending in the season.
The only fish where it's true that you only find the bigger ones at greater depth is the dusky grouper. The most prized fish for Greek spearfishermen and threatened in its existence.