In this case "the algorithm" is the fly in the printer from the '85 movie "Brazil". Except these are real stories, it's absurd.
Sure it is; what inputs go into producing the ultimate decision and how those inputs are processed is an algorithm problem. Particularly, whether and when output is sent to one or more humans requesting input, and how input from those human(s) is factored into the ultimate decision is an algorithm problem.
The fact that the decision algorithms at issue often do not involve human assessment as part of the input set when they should is a defect in the algorithms' fitness for their intended purposes.
If you're designing a process where you take the output of a program and delete all records flagged by the program, you can add a human validation step in pretty easily. Companies often have process engineers whose job it is to do exactly this: and when you're talking about data management, process and governance are very important.
Yes, this is slightly more expensive than using an algorithm alone. But it could actually end up being cheaper in the long run if law suits are involved. Sloppy data governance causes all kinds of problems that are hard to quantify numerically, and that's the root cause here - not bad algorithms. At the end of the day, every algorithm is going to produce imperfect data: they're based on simplified logical models of real world systems. Recognizing that algorithms are imperfect is a key part of knowing when and how to use them.