Thanks for the link. However, after reading the whole section I am left believing that using the API of an AGPL project would indeed be considered "incorporating" it.
Note how the "arms length" usage, as described, mentions completely separated software such as a shell and a notepad application.
The separation between a shell and a notepad (i.e. different applications altogether), or a kernel and a compiler (i.e. the base system and an application) seems to me clearer than the separation between an application and a library that it uses (i.e. the library is being used as part of the application in order to fulfill a feature).