It is easy to get
most of the flavor profile of a natural flavoring using a single pure synthesized molecule. But natural flavors have a host of other "support" molecules that add to the flavor, like adding harmonics to a musical chord.
For every molecule like vanillin, which is a powerful enough component of vanilla that it can often stand in for the whole, there are dozens of molecules that produce variations in flavors when combined. Most humans can't tell the difference in a blind taste test in baked goods.
Furthermore, those support molecules can become easier or harder to taste in the presence of proteins, sugars, or non-aqueous solvents.
So if, for instance, you want to make your artificially flavored vanilla ice cream taste exactly like naturally flavored, the aromatic additive cocktail you must use in addition to the vanillin will need to have a different composition from another food-chemist's concoction for vanilla-flavored sugar cookies.
But even then, you will have to decide what kind of natural vanilla you will choose to mimic, because the country of origin of cured vanilla beans can be discerned by professional tasters and with 100% accuracy by chemical analysis!
It's only moot because it is possible for people to prefer the taste of the artificial flavoring over that of the natural flavor, not because they are indistinguishable from each other.
And as I mentioned elsewhere, compounds purified from genetically engineered microbes can still be called "natural". That seems to be a clear case of pitting the letter of the law against its spirit.
Edit: I mean natural in the vernacular sense, not in regard to whatever is allowed by food labeling laws. That sense is "natural", in scare quotes. Natural coconut flavoring can only come from actual coconuts. "Natural" flavoring can come from the bark of an unrelated tree, beaver butts, engineered microbes, mushrooms, or anything else that could grow in the wild if it were released there. Artificial flavoring comes from a biochemist with a tank of ethylene and a CRC manual.