The answer to your question is that no one really knows. When a country of origin is given one might assume that the perfume contains an essential oil or other natural material (for example, French labdanum resin, Indian patchouli leaves, etc.), but it is also possible that the perfume contains a synthetic accord formulated to smell like the real thing. In some cases it is the real thing, in others the accord. Some manufacturers are more realistic and forthcoming than others in listing their note pyramids. Most note pyramids, for the sake of brevity, omit many of the accords, aromachemicals, or natural materials that go into the perfume, listing only what the perfumer or advertising copy writer wants you to pay attention to. I think the best overall strategy is to regard the note listings as a general guide to some of the odors that you might detect in a perfume if you consider it analytically, not the actual materials that go into its production. As you point out, you may not detect the individual notes at all because several of them fuse perceptually to form a new and unique odor. After all, that's what an accord is all about and what a successful perfume accomplishes on a larger scale.
I think the bottom line is that each person smells something a little bit different in a given perfume, and everyone is "right", so trust your nose more than the note pyramid and enjoy your sniffing!