It seems to me there are two issues here: what are your AGPL obligations with respect to this binary, and do those obligations extend past that software package?
Your AGPL obligations with respect to the binary are clear, from AGPLv3 s13:
Notwithstanding any other provision of this License, if you modify the Program, your modified version must prominently offer all users interacting with it remotely through a computer network (if your version supports such interaction) an opportunity to receive the Corresponding Source of your version by providing access to the Corresponding Source from a network server at no charge
You are not modifying the covered work, so I don't see that this clause is operative in your case. If you were to distribute the unmodified binary, you'd still have the normal GPL source-provision obligations; but you're not doing that.
As for the AGPL obligations extending to cover your software, the FSF is pretty clear that using an AGPL binary "by issuing some well-formatted shell execute statements" doesn't make your work a derivative of the AGPL code:
By contrast, pipes, sockets and command-line arguments are communication mechanisms normally used between two separate programs. So when they are used for communication, the modules normally are separate programs.
As long as you're not passing complex structure (including but not limited to pointers to regions of shared memory, or files embodying complex structure) it seems to me that you should be fine. Nevertheless, IANAL/IANYL, so you may wish to get professional legal advice before betting a company on this.
