Plus the fact that natural EOs shelf life is not as that of synthetic EO (1), many of them have a very marked indolic / fecal notes (2) and their longevity is quite limited (3).
I had / have four "all natural" scents in my wardrobe:
1. The content of a bottle of Lavander water got spoiled after five years of storage in the right conditions. As a result, you could see the EO and the alcohol the same way water does not mix with oil. A stronger and putrid indolic note remotely similar to that of raw lavender was the sole note present in what was left in the bottle.
2. A lavender water made in a lavender destillery in Córdoba (Argentina) is well known for its disgusting top note, and as the manufacturer claims, it is because of its natural properties. I have two fragrances made by local aromatherapy companies claiming to use 100 % natural EOs, they all share the same characterstic - offputting top and middle notes, nice base notes. They are sold to be worn for their healing properties. A third one, which is actually a scent for men, has very harsh and pungent top notes, to the extent that the descriptor "aromatic" seems lame in comparisson.
3. Except for one of these blends contanining patchouly, they are all fleeting, detectable to my nose for no more than one hour.
Now, IMHO there is such thing as "synthetic smelling"; unfortunately, I cannot describe it clearly. Still, up this point I can detect synthetic feels very pungent to the nose, notes are unbelievable long lasting and they feel exagerated. Take Ferre's Bergamoto Marino, it has the structure of an Eau, but the blend feels like the notes of an eau that have been taken to their limit. Same with the "green" template in style during the 1990's, which is originally bergamot (CK's Eternity) or the fruit and gourmand accords present in Rabanne's 1 Million.
I might be confusing harshness with synthetic, but as far as my nose-training goes, the intensity of certain notes makes it feel like it.