I was the one who wrote the first quote you gave.
And you didn't quote what I said after that:
"She may be relatively unknown to the general moviegoing public, but that does not mean she is underrated. Her father is considered one of the greatest directors ever! That alone means every one of her films gets lots of attention. My understanding is she is well-regarded by people in the film industry, and that's the under/over-rated they really care about."
I distinguish between unknown to the public and underrated. They are not the same thing. Sophia Coppola, who was the subject of that question, may be relatively unknown to most people, but if you write and direct a film that wins for Original Screenplay and is nominated for Picture and Director, you are not underrated by the critics.
I think that's the crux - are we talking about the opinion of the public or the opinion of the critics? Awards are decided by critics and members of organizations (who are usually either critics or have professions in the film industry), but if you ask a random member of the public who watches 1-4 movies per year to name some directors, here are the usual suspects: George Lucas, Ron Howard, Steven Spielberg, Alfred Hitchcock, and maybe Kubrick, Francis Ford Coppola, and Scorsese. Those may be the best known (arguably of all-time) and are not underrated by anyone, but that doesn't mean someone who watches less than a half dozen movies per year is really that well versed in directors.
It was pointed out in the original question that Sophia Coppola has only directed four films and is therefore underrated. Yes, but Virgin Suicides is one of her other directorial efforts and it is generally praised by critics and people who have seen it, as well.
By the way, as to the criticism of bringing Coppola's father into it, I stated, as you can read above, that because of her father, her films garner automatic attention. That's simply true. I did not say her films are automatically good.
You state, "My definition of underrated; not being consistently recognized by movie fans." And I have stated my definition is closer to looking at what the critics say (though I did ask earlier in this whether we are looking at fans or critics, and gave reasons for why I think critics should be favored (ie. most fans are not well-versed in directors)). So as far as I'm concerned, we can agree to disagree. And really, it is not that big of a deal :) Coppola is hugely underrated amongst the public - I completely agree with that. Amongst people who study film or follow film/directors closely, I think she is well-regarded and not underrated.