As a Greek-American who grew up speaking both, I agree with this, although in my case I'd characterize it to some extent as more "old-fashioned" than "academic". I learned Greek primarily from my mother, but it was especially reinforced by my grandparents (because they didn't speak English, so I had to speak Greek with them). As a result my level of fluency with Greek of the 1930s-70s is better than with contemporary Greek, especially when it comes to colloquial terms and nuances like intonation, pauses, implications, gestures, etc.
I think the first time this really became clear to me is a few years ago when I was on a bus in Crete full of elderly people (mainly 80+), and I realized that listening to their conversations, I felt really 100% fluent in Greek down to the last nuance. Usually, when surrounded by Greeks who are younger, I think of myself as more like 80% fluent and miss many nuances, so being on this bus full of grandparents felt like some kind of fog was lifted and my comprehension went up to near-perfect.