Reasoning: Homer and Fish

I finally arrived in Greece for the first time a few days ago. On my first night, I was sitting with a collection of graduate students who were studying at the American and Canadian schools here. This question came up at dinner: "why do Odysseus and his men never eat fish?" It's a pretty good question, especially considering that Odysseus and his men are starving when his comrades resort to eating Helios's cattle. The same can be said, even outside of the Odyssey. When Agamemnon and his men are marooned on an island by lack of wind on their way to Troy (as retold in the Agamemnon), they too begin to starve.

Today I was reading Pomoroy et al.'s Ancient Greece (now in it's third edition), and they claim that "because fish are not abundant in the Mediterranean, they were usually eaten as a small 'relish' with the meal" (Pomeroy et al. 2012: 19).

Is this true? There seems to be seafood on menus in Greece today (including fish). Is the Mediterranean really short of fish?