There is a little bit of difference between the velocity, and more importantly the performance, of a Berger bullet at the muzzle and one at 620 yard - and no animal ( except man) can be considered dangerous at that distance.
I don't know your load but what do you figure the velocity of your bullet was when it struck the bear at that distance? I would guess it under 2000fps and about the same energy as a 30-30 ? You proved once again that 30-30 ballistics and soft cup and core bullets is all it takes to kill a bear under ideal conditions - but for those of us who believe in stalking up close on dangerous game I prefer something with just a little bit more reliable and proven performance.