[assbuttbuttass]

By my reading, the AGPL doesn't define "distribution" at all. It defines "conveying":

    To "convey" a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying

This definition specifically excludes networked API access.

Here's what the AGPL says about network access:

    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, through some standard or customary means of facilitating copying of software. This Corresponding Source shall include the Corresponding Source for any work covered by version 3 of the GNU General Public License that is incorporated pursuant to the following paragraph.

It only applies if you "modify" the program. Does creating a proxy service count as modifying the original program? I think it could count as a derived work, but I would be very surprised if that counts as a modification.