My description was a little too short and poorly worded. I meant if you implement the service using the agpl project, and only expose the API over the network,

My description was a little too short and poorly worded. I meant if you implement the service using the agpl project, and only expose the API over the network, the source becomes subject to the same terms as if you had distributed the service binaries. So in this case whoever does own the service has the liability.