Yes but the packing density of flour varies cup to cup, within the same measuring cup, resulting in different amounts of flour.

> J. Kenji Lopez-Alt, the managing editor of the blog Serious Eats, once asked 10 people to measure a cup of all-purpose flour into a bowl. When the cooks were done, Mr. Lopez-Alt weighed each bowl. “Depending on how strong you are or your scooping method, I found that a 'cup of flour’ could be anywhere from 4 to 6 ounces,” he said. That’s a significant difference: one cook might be making a cake with one-and-a-half times as much flour as another.

So you have to carefully scoop precisely the same way every time to even be close to accurate??

> 2 cups of flour works regardless of the size of your cup

This couldn't be more wrong and no serious baking is done by volume for dry ingredients (flour, yeast, sugar, salt preferments, other additives).

EDIT: It is clear from your other comments you almost certainly know what you are doing, but this particular part is very wrong. You can't measure powders reliably by volume, regardless of sifting, tapping, or tamping.

One of the major problems with this theory is that "cup" doesn't have any standard definition - and measuring scoops marked as "1 cup" - can be anywhere (ignoring outliers) from 240, 236.6 or 227 ml. So - ignoring the fact that when you scoop flour - the same scooped "cup" can vary by as much as 10-15%, the cup itself may be off by 6%. And you are never quite sure which cup the original recipe maker was using.

This is why any half-ways sane baker works off a scale.

No, in the imperial system they're based on proportions. In the metric system they're based on multiplying or dividing actual weights.