This is an incomplete thought experiment. It should go without saying that it isn't rigorous or backed up by anything except 'common sense', whatever that is. In this post I'll examine a scenario by changing variables individually in series. Is there an alternate interpretation of the scenario? Are there variables I haven't considered?
Putting this complex idea into a succinct form has proven quite difficult. I hope the reader can see wherein I attempted to justify my reasoning.
Let us first make an important distinction between what I will call real threat and felt threat. Real threat is when there is an objective reason to believe that some harm is immanent. Felt threat is the subjective emotion of fear, whether because of an objective reason or not. I will try to keep the delineation between the two clear.
Is the scenario threatening? I think that most people, myself included, would experience feelings of threat. The factors that make it threatening seem to be that it is dark, isolated, sudden appearance of a man who is unidentified. Taken together this seems like a classic mugging scenario. We can accept that given this amount of data there is real threat. But how does the assessment of real threat change as additional information is known?
Variable: Time. The longer that the two people walk together without any assault the less that there is reason to believe that there is a real threat. It was the sudden appearance of the man that indicated immanency. As time passes and no aggression occurs the real threat rapidly decreases. The felt threat may very well remain but without rational justification.
Variable: Distance. There are unspoken (but highly studied) rules of personal space. The 'comfort zone' varies among different people based on diverse factors but the two most influential factors are the population density where the individual lives, and how many people are currently nearby. If the person first hears the sound when the man is 15 meters behind them there is significantly less threat potential than 5 meters. In this situation 1 meter seems to be quite threatening. Threat is more if the Man is overtaking the Person, less if he is falling behind. It is worth noting that if you don't notice someone overtaking you until they are quite close you may become startled and be quite justified in experiencing threat that goes away rapidly as they pass you without incident.
Variable: Other People. The isolation is what makes it threatening. However, more people might increase threat, up to a point. A person walking opposite direction slightly decreases threat. A person walking same direction decreases threat by a moderate amount. A person walking same direction but behind increases threat additively due to danger of being outnumbered in the event of an assault.
Variable: Location. If the location is unfamiliar, threat would be at maximum. If the area was highly familiar then it would be lower due to higher likelihood of escape or assistance due to local knowledge.
Variable: Sex. The Person's sex doesn't influence threat directly. Rather, traits that are prevalent to each sex change the level of real threat: primarily size and strength. On average women are smaller and have less upper body strength than men. However similarly proportioned men and women are subject to similar degrees of real threat. Worth noting is that there are martial arts disciplines where smaller size gives a large mechanical advantage.
Variable: Preparedness. Having choices drastically decreases threat. There is no evidence that the Man is armed, but in a threatening situation he must always be assumed to be so. If the Person is unarmed then that puts them at a significant disadvantage, increasing real threat. If the Person has some form of self defense training (even just athletic training), pepper spray, a firearm, or a combination of these things real threat decreases because of the increased expectation of escape and/or reciprocation of force.
Perhaps some day we can expect that there be no reason to be rationally threatened in a real sense. It may be that there that time will never come. Until then it is unreasonable to expect to go through life without situations where you experience threat. We are hardwired for fear, and the experience of fear still serves us well today. It makes sense that by reason we can relegate fear into a subservient position.
Of all the factors that influence real threat only preparedness is something that can be controlled by the Person. A responsible person takes the steps necessary to ensure their own safety, survival, and genetic increase. This is empowerment by action. To argue for, or desire a state wherein an individual no longer is responsible for themselves is to move toward more victimization and disenfranchisement.
Individuals should examine carefully the situation that makes them feel threatened. Is the situation objectively threatening? If not, then they should discard or suppress the emotion as the byproduct of the modern remnants of our ancient reptilian brain.
If the situation is indeed objectively threatening then there are myriad actions that can be taken to reduce the real threat of that situation, about 30 have been illustrated above and these only scratch the surface. With so many options available it isn't reasonable to expect a rescue. Rescue is a pleasant surprise, not a right.
A properly prepared individual reduces the real threat of the most common situations to zero. Any left over irrational fear is their own responsibility - not the fault of the person they perceive as being threatening. This is what personal responsibility is about.