Unless it’s icy out, you have to swerve, or you’re being tailgated...but yes, stopping (or at least attempting to stop) is the best decision from a liability perspective.
Well that's when you're grateful that along with your forward collision prevention, your car's ABS and electronic stability control systems are also still enabled.
As for tailgating, this seems to be a problem with U.S. attitudes, not vehicle mechanics. Stop making it acceptable to tailgate! If you're close enough to the vehicle in front of you that any significant braking on its part will cause you to hit it you are too close and it's your fault if you hit it.
Legally, in most (if not all) of the US you /can/ be cited for tailgating (the laws require a minimum following distance).
Reality is that the traffic cops seldom ever cite for tailgating in general. If one were to see a citation for such, it is likely after an accident where the officer can deduce that the cause was "following too closely" and so they then issue the citation.
In Australia, if you are the rear vehicle in a rear-end accident you are automatically at fault in almost all circumstances. The only exceptions I know of are if the front car pulled out immediately in front of the rear car, or if the front car was reversing.