The Piri Reis map does not Brazil at all! It shows Patagonia in Argentina! It is out of scale but it is not the issue. Your article sets up a straw man. But the author himself is unaware of what the map shows.
As for the rest of your post, you resort to the tiresome "read this book and it will explain" garbage. No. YOU explain it. What does Jared Diamond's book have to do with this discussion? I have read that one.
If you want to say that this or that is wrong then explain how it is wrong. Don't say it's wrong and say, "Just read this book." If you have a case to make then make it. Right now your case is: "You're wrong because I say so."
Please explain specifically what is wrong and why. We can prove everything is wrong with sweeping generalities.