The idea is that *most* of the time a brown bear is going to be attacking a human because they feel threatened or for something like protecting cubs. Since the attack is defensive by playing dead the person convinces the bear they are no longer a threat and hopefully the attack will end. However if the attack does not end then the victim is advised to fight back, for whatever good that is going to do.
Black bears are different in that they are generally much more skittish and will almost always flee from an encounter with a human. If a black bear attacks it is not going to just be roughing you up, so the advice is to attempt to escape or as a last resort you should fight back. Black bears are relatively small so fighting back can be more effective as well. Playing dead is not advised with a black bear attack.
Polar bears are adapted to an environment where they need every meal they can get to survive. If you encounter a polar bear it is going to be trying to eat you and your only chance is to escape or have a firearm that can kill the polar bear. They are very large and fighting back with just your hands is basically useless, and playing dead will just let them eat you in peace.
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