Intuition is important in science.
Yes, but scientists recognize that intuition isn't sufficient.
Note that he said "SOMETHING like it must be true"
Just because something is intuitive does not mean that the truth is anything at all like the model.
A flat world with Greek knowledge of such topics is, intuitively, similar to the modern day view.
Exactly. Intuitively it's flat, but that's wrong. Nobody has fallen off any edge.
In any case, you misunderstood; my comment wasn't written clearly. I was referring to the idea that reason alone is sufficient to find the truth. In fact the ancient Greeks did eventually figure out that the world was round (see: Eratosthenes) to great accuracy, but they did it empirically.