Your fists are not the tools of "deadly violence" unless you are Chuck Norris. Martin proved he is not Chuck Norris because he died during a melee encounter with an inexperienced fighter.
And again--if the person following you has a machete instead of a gun do you feel more or less threatened? A gun is versatile and effective at range--and up-close if it happens to be in your hand already. A machete is useless at range and its effectiveness both as a tool of intimidation and as a useable weapon is completely eliminated if the target simply runs away.
If the person with the gun cuts off your escape and you suddenly find yourself in melee range it is the only option. Unless, of course, you want to bet your life on the mercy of the person chasing you or their inability to shoot a moving target.And if nobody here would personally confront their follower, punch them in the face and then smash his head against the ground, then it cast serious doubts on whether it was a reasonable response.
You may be perfectly fine with doing whatever your confronter says and hoping he doesn't shoot you anyway. Some of us would prefer to have control of our lives and take the advantage of openings when they arise.