I don't know if that was a typo, but letting users run the software on your computer, isn't 'distribution' in the usual sense. What you said sounds true of the GPL, but doesn't give a complete account of the AGPL.
From the FSF: [0]
> The GNU Affero General Public License is a modified version of the ordinary GNU GPL version 3. It has one added requirement: if you run a modified program on a server and let other users communicate with it there, your server must also allow them to download the source code corresponding to the modified version running there.