Exaggerated conclusions by the writer. The fact that ONE PERSON figured out part of the puzzle of the round earth didn't everybody (a) either knew about the theory or (b) believed it!
The Ptolemaic system (2nd Century AD) assumes that the earth is a sphere, and that system was widely accepted throughout Europe from ancient times through the middle ages and the Renaissance, until it was replaced by the Copernican system. So I don't know whether peasants knew or cared that the earth was round, but educated people in general did.
Actually, the myth of the flat Earth being disproved by Columbus was invented during the 19th century. The spherical nature of the Earth was common knowledge at least as early as the classical Greeks. The fact that the shadow of the Earth on the Moon was circular is one thing that tipped 'em off.
Herodotus had a screwy idea about the Sun (seen in his idea about the source of the out-of-season flood of the Nile, described after he described the correct reason and two others), but knew that the Mediterranean and Atlantic connected with the Indian Ocean (and he doesn't differentiate between the Persian Gulf, Red Sea etc, and the Indian Ocean), and he wasn't the discoverer of that fact, merely reported it 2500 years ago.