I want to preface this by mentioning I didn't read your entire post, but just these scenarios.
Given our current design, the first scenario would not play out that way. Because the robber had his weapon out, his stress level would be maxed out as soon as he equipped the weapon. Therefore, he's immediately vulnerable. You on the other hand don't have your weapon out, and thus you have a decision. With the weapon aimed at you, your stress is going to rise very quickly. You have only seconds to respond. If you were to surrender (put your hands up), your life is no longer at risk but you can be robbed. If you decide to fight back you become immediately stressed by unholstering your weapon. Chances are that you'd be shot before you had time to fire back, if he was already aiming at you. If you took cover and then pulled it out you might have more luck.
A melee weapon, as is mentioned in your second scenario, works similarly (but might not raise stress quite as quickly). That is, when he pulls out a melee weapon in front of the other guy, that guy has only seconds to make the same decision. He can run (which causes stress to go up faster) in hopes of getting away but also making himself vulnerable, surrender to save himself or fight back.
The goal of the system is two fold: first, to reduce random player-killing, and second to give you the option of fight, flight or surrender.