That visual is pretty striking. Another way to think about how screwy it is is simple division: 1000 people divided by 42 decks means an average population of 24 per deck. You could put the entire compliment of a deck into one room, comfortably. You'd practically never see someone else in the corridors unless they were coming from or going to the same place.
I don't think anyone ever gave an official crew figure for the KT Enterprise. There might've been a tie-in website that had something around a thousand, but the closest thing I can recall specifically is a comic book saying the cyborg crewman Science Officer 0718 gave himself that name because he was the 718th member of the Enterprise's crew. Of course, the KT Enterprise actually is filled with giant open spaces and machinery, and isn't an endless warren of rooms and corridors, which the -D is always depicted as.