Heya,
It's not true.
What is true, is that a smaller, lower resolution image will appear sharp relative to the viewing size. That's all.
Is it a good idea to shoot at lower resolution? People have reasons. If it's just for facebook or low quality print where quantity is more important to the shooter than quality (this is true for some reporter types who upload literally as they shoot, so they shoot lower resolution JPG to make mass transfer faster from a wifi source in the field), then it doesn't matter. But for someone wanting to keep the best original image they can and downsize, etc, later, then there's no sense in shooting anything other than the largest, most information containing image you can. It's not like space is costly or limited these days.
Very best,