Name a product that is touted by its advertisers as unscented, yet actually has a scent.

Everything has a scent. They are a bunch of liars. A new question from me.

"All of them."

I don't want to rain on your parade, but this site .....  https://birchhillhappenings.com/unscented.htm  ...  has some interesting thoughts on the matter ... like:

There are no absolute definitions set by the FDA (Food & Drug Administration).

(* There are no official, government definitions for these terms.)

Every substance on earth has a smell. Even our unscented products may have a slight smell.

Etc.

Scents that present themselves naturally do not have to be listed as fragrances.  Unscented described a product where no fragrance was added.  In the realm of harmful chemicals, fragrances are high on the list.