I'm trying to read the AGPL in the most tricky possible light to see where the exact boundary is.
From what I think you're saying, I could make a service that uses PgDog behind the scenes, which would mean I could modify PgDog without releasing the source code.
However, given most people making PgDog As A Service wouldn't put PgDog directly on the internet, but would put it behind something like HAProxy, or perhaps even a REST API that takes in a SQL query as text and runs it on PgDog. Would either of those options then mean they could modify PgDog without releasing the modification's source code?