That's not a reason to use the handbrake over the brake pedal. Typically the brake pedal is more effective (all wheels, ABS) than the hand brake (sometimes 2 wheels, probably no ABS). The handbrake is just for emergencies and parking.

When I learned to drive in the US (Washington state) I received advice similar to that, however when I took lessons in the UK, I was advised that when you are rear ended, you will have a hard time keeping pressure on the break pedal so you should do both.

Fair enough.