I think so. I live in a fairly big city and it's the same here. Excellent public transport, not so many cars around. Walking to the subway station is already 600m. Inside the subway system one can walk a lot for connecting lines. Even if I did have a car it would be a few blocks away in some parking garage. It's not like we have car ports or driveways here.
3 km is only 1.9 miles, or just over half an hour of walking for most people. If you have a 0.95 mile commute you've already hit the several kilometers per day bar.
Anecdotally, when I go out there for business events the locals invariably suggest walking if the distance is ~1 mile or less. Do that there and back and you've hit 3 km walked on a single event.
In Manhattan at least (this is different elsewhere in NYC), as a general rule, 20 city blocks (going from 44th Street to 45th Street is one city block) is approximately one mile. Three Avenue blocks (e.g., from Fifth to Sixth Avenues, etc.) is also approximately one mile.
Walking ten blocks (~800 meters/~1/2 mile) to do just about anything is pretty normal, and walking further is pretty common too. If you note that's one-way, the round trip is ~1.6km and multiple jaunts daily aren't uncommon.
While street lengths are different in other boroughs, depending on where you live, you may well walk several miles every day. Or you may not. Folks who live in the North Bronx, Staten Island, Eastern Queens or South/Southeastern Brooklyn may well use motorized vehicles for many purposes, as the layouts are more similar to US suburbs than other places in NYC. YMMV (pun intended).
I'm a native NYer too. And three was generally the rule of thumb AFAIK.
That said, as we both know, avenue blocks are of varying lengths. So depending on which avenue blocks we choose, we're probably both right and both wrong at the same time.
You'd expect that if you assume that US cities are all pretty similar in their car-centeredness, but NYC and LA couldn't be more different in this respect.
I don't think I can take this claim for granted.