We know from studying human DNA that the population collapsed some 70-75,000 years ago to perhaps as few as 40 people. It now seems unlikely that the Toba Event was responsible for that collapse. So what caused it? I don't know, but at about the same time, a rogue star passed very close to our solar system. So far, the evidence doesn't seem to indicate it, but its early days yet, and with the time frame's being so close, I wouldn't be surprised if there didn't turn out to be a connection.
I never even considered Miley Cyrus. Generally, a performer has to have talent at some point to ever be considered a 'star' -- and Miley Cyrus's only talent is doing an impression of an anorexic beagle on its hind legs.
I wouldn't think that there would be much gravitational perturbation of the Earth by Scholz's Star passing at 0.8 light-years; the star's influence on Earth would be far, far less than Jupiter's, and that's pretty small. However, I have to wonder if the sun's magnetic field could be altered by another star at that distance, changing the solar winds and perhaps influencing the climate on Earth.
You're forgetting the Oort Cloud, which it would have passed close to, if not through. Depending upon the direction from which it approached, and what the orbits of the bodies in the cloud are like, it might very well have sent comets in our direction.
But we haven't necessarily been looking in the right places for it, either. We're still trying to figure out if the megafauna in the Americas was wiped out by a comet exploding in the upper atmosphere. The evidence for this consists of particles embedded in mammoth fossils. The jury's still out on the subject if its conclusive proof (one paper proposed the idea, another paper refuted it, a third paper has refuted the refutation, last I heard) of what happened. If enough comets exploded in the atmosphere, they could cause the necessary climatic upheavals, without ever leaving an impact crater, and if no one thought to look for the right kind of signs indicating that this is what happened, we wouldn't necessarily have spotted them by now.
Exactly how fast do you think comets travel? Anything disturbed in the Oort cloud 70,000 years probably won't have reached the Kuiper belt belt yet.
This where you get into things like orbital mechanics, angular momentum, and the imprecise nature of genetic dating just for starters. Genetic dating is an imprecise science, and can have varying margins of error depending upon what you're looking for, and how far you're going back. The margins of error I've seen for the "Toba extinction" are plus or minus 2500 years. The date for when Scholz's star passed into the Oort cloud is probably more precise. Of course, we're not entirely certain of the size of the Oort cloud, so there's some variability as to exactly when the star would have reached it. Nor do we know if that star has its own Oort cloud. Our Oort Cloud is thought to start between 0.03 and 0.05 lightyears from Earth. At its present speed of 35K MPH, it would take Voyager 2 10,000 years to travel half a lightyear. It, however, is going "uphill" and fighting the sun's gravitational pull as it leaves the solar system. On object headed into the solar system would gradually pick up speed as the sun pulled it in. Without more information, its impossible to say when Scholz's star would have begun perturbing things in the Oort Cloud (if it did), what would have happened to them, and the like. Remember, what I'm suggesting isn't terribly different than the Nemesis hypothosis.