After the huckleberries are done late august I find they come lower between 3-4000 ft.
In response to this and the OPs question... some bears move down to 3,000-4,000 feet, yes.
At the same time, there are thousands and thousands of bears who would never consider going that high. You might be surprised how many bears live down lower and are out and about through November.
Oh I have no doubt. That's just the elevation my families property is at so that's where I hunt. In that area that's just what I experience. I still get bears on cam where there are berries just for that area once they are done I get 3-4 times as many different ones on cam.