https://en.wikipedia.org/wiki/Tueller_Drill
The drill is considered a fairly basic level training for quick target acquisition at close range. The original study and all subsequent tests assume that the attack immediately ends in failure if the melee man gets in touching distance. The issue is even with a skilled melee fighter the guarantee of getting a kill without the resistance of the gun man. Likewise, it assumes that all police are untrained in hand-to-hand combatives and that a single touch from a outstretched arm will result in the gunman instantly being crippled and incapable of fighting or is otherwise incapable of resisting. Which is kinda ridiculous.
Even from a undrawn position from exactly 0 feet to cross, against a UFC fighter, etc. A gun man still has the clear potential for killing their opponent despite what the Tueller Drill wants you to think. But this isn't even considering-
That in video you provide it shows the mythbusters cocking the gun, only in a garrison, range, and under very specific situations involving a lot of politics are guns kept in Condition 3/Amber. But in every other environment with nearly every police agency and military agency the condition that is standard is 2 or 1 if there is any remote chance of a hostile confrontation. This means at most the gun man just has to pull the weapon out, flip the safety and begin shooting. As Glocks don't have a manual safety, revolvers don't have a manual safety, springfield XD uses a grip safety, and one of the most asked questions about the S&W M&P shield is how to remove the manual safety the act of flipping the safety while drawing may not exist.
More than likely the melee man is going to be facing something more like this.