Rich, you are exactly right, with one exception.

There WAS a book written that claimed people of Columbus' era beleived the earth was flat.
George Washington Irving wrote a book in the 1800's that said this was the case. It, of course was wrong, but the book was very popular with history teachers. That Irving myth is credited with the single writing that caused so many people to come to this misconception.

Scientists, astronomers (even astrologers) and sailors long before the 1400's were well aware the earth was round. Since the egyptians had been studing the stars and moon, etc, for over 5000's years we knew. (My guess is that it was probably realized long before that by most societies.)

This is probably one of the most prolific urban legends around.

Jim