This is such an odd statement. I think the article makes a good case that in this context, metrics serve as something like the opposite of a tool - a trap, something a person or group uses that takes them something other than where they intended. Now approximation, generally, is something like a tool but it can be used well or badly.

Now, a bureaucrat or someone who want to "just get stuff done" may use a metric to get people moving without caring exactly where. But that's still with a human context, not an AI. In an AI context, a metric can run a plane into the ground or more or less anything.

IE, it's only some of the contexts (racist AI) where metrics have a social content.

The point about corner cases is reasonable but it's easy to by analogy that human correction can't keep with the problems metric yield for complex spaces; just consider how a ten dimensional cube has 2^10 literal corners and AI more or less operate in spaces with many more dimensions (of course not all "corner cases" are literal corners but there's a similar problem of intersecting "areas of concern" or whatever one would want to call them).