I have never once encountered this misconception until now. Every explanation of deep learning I’ve seen begins with an explanation of the origin of the phrase.
A few weeks ago someone submitted an entire article to HN that consisted of someone complaining that deep learning wasn't really deep, in the deep & meaningful sense. They clearly misunderstood. Was pretty funny.
It would not be nearly as well funded were it not for this misconception on the part of budget holders, and everyone involved in ML knows it.