Barnard’s star is moving significantly faster - 140km/s vs. 80km/s relative to the sun.
Scholz’ star is *tiny.* The entire binary system is < .15 the sun’s mass. The apparent magnitude of the star when it was @ .85LY from the sun was still 20 times too dim to be seen by the naked eye.
The math definitely works out - Scholz’ star would be 18.6ly way if it was moving away from Sol @ 80km/s relative velocity.
The objects were too low-mass to have any significant impact on the Oort Cloud, much less the Solar System. The binary system would have likely gained +/- .25km/s on approach to the sun, only to lose it again on its way out.
Wouldn't that depend entirely on how close they got to any individual Oort cloud objects?
Would a 10 km near miss of a 1/8 solar mass, red-hot object affect a cryogenic ice ball's path?