I think you're combining "algorithm" and "process" which is something programmers often do (because for a programmer, they are the same thing). Businesses tend to think of "algorithms" as black boxes where you feed a data set in one side and get a modified data set out the other. That data is then incorporated as part of a business process.

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.