I think we can knock this down directly. The predicted semi-major axis is 1.5 light years. It was plausible at the time it was written that such an object could remain hidden. It is no longer plausible that a black hole with the required minimum mass to form would have escaped decades of automated asteroid search. It's too close, has too much parallax, should have too much transverse velocity, and would have shown up as gravitational lensing in the asteroid searches by now. They're looking for objects that aren't the same from frame to frame. This would trip the detectors.
The first-pass processing for asteroid search is simply take two plates of the same part of the sky and diff them by something that's little more than XOR. You now have bright spots where something moved. These are checked against a known table of foreground objects, and anything not matched gets looked at by a human. An unexpected gravitational lens will show up because it didn't cancel between the frames because the light magnitude was too different. If it's not dead-on (and this will be most of the time) it will also have moved.
The orbital mechanics involve in the capture would greatly distrupt the Sun's galactic orbit in the plane of the capture. We note that life appeared on the Earth's surface almost as soon as it was sufficiently cool, and was not fried by the galactic radiation. This in turn requires the sun to have the Z axis oscillation around the galaxy it has or smaller; which constrains Nemesis to be on or near the galactic plane.
But I've got a hole I can't close. If we ignore the normal Nemesis postulates enough we can end up with it being the Sun's companion for the entire time. The typical capture process should be disruptive to planetary formation around the embryonic Sun but the postulated orbit is more than far enough away to avoid this problem. This requires an exotic capture method, but we were most likely going to end up with one anyway.