Lousy with Stars

"Gee, the sky is lousy with stars." So said the father of one's of my wife's friends just before proposing to the mother, and it could be the first, might be the only half-romantic thing he said in his life. For me and Hilary it was a favorite quote for a while.
The quote presumably occurred in the late '30s, early '40s, and we were citing it in the early '60s. By the later '60s I was beginning to hear things quantified that had formerly, for me and my habits, remained unnumbered. Thus I heard that there are only 2,000 stars visible to the naked human eye at the earth's surface.
I could have heard that from Bucky Fuller. I could have read it in Isaac Asimov. Guys like Nigel Calder and Carl Sagan said those sorts of things since then.
Now I think to ask other questions around that fact, about that fact. First I presume the figure is a round number: if one actually counted 1,999 or 2,001, one would say "2,000," wouldn't one? But who did the counting? Using whose eyes, whose counter? Were they counting what the eye takes in in one glance? or were they counting 360 degrees, horizon to horizon to horizon? How many stars are visible from earth throughout the night: every constellation and everything in between? And are we sure it wasn't a camera lens and not an eye that did the seeing?
Whatever the answers, I'm satisfied that the quantity will still be in four figures, or a low five. That's quite a contrast from the numbers that Sagan would intone for his Cosmos series: hundreds of billions of stars in almost any of hundreds of billions of galaxies: with previously uncounted stars and galaxies coming into view almost daily: these days.

Now, I'm going to be using those images shortly in the post I'm about to write -- Finite Casting Call. But I post this first and separately: mainly to ask a question. Does anyone out there have answers for any of my questions? Do we see "2,000" stars in one look? Or do we have to be a fish-eye, lying on our back throughout the night?