Yup, they are rich. It's mostly the Collosus of Rhode though. Sea trade is the best way to make money in the game. The Colossus gives 40% extra. It's ridiculous. Maybe 10% or 15%, but more is just too much. So if you want money, just go for the Colossus.
The Greeks would still be rich without it, but a bit more in normal proportions to the rest.