True, but it’s interesting… some of those new world plants spread so quickly that, for instance, many New World foods were first introduced to the US from the Old World, and knowledge that they were actually New World would have been quite limited.
For instance, chile peppers spread from South America so quickly that subsequent explorers of Africa, China, etc. misidentified them as being native to those and other places.
In the US, even among native communities, chile peppers arrived largely with slaves from Africa, and were thought of as exotic.