There is nothing weird about this paper, the math works, and primordial black holes (which is a astronomical term, not just a plain English descriptor) are not

There is nothing weird about this paper, the math works, and primordial black holes (which is a astronomical term, not just a plain English descriptor) are not the thing you're clearly thinking of given your rant. Checking to see if outer planetary motion can be explained in terms of PBH and working out the math as part of that is perfectly normal astrophysics, and good science. Read the paper, it's perfectly fine =)