So yes, it "triggers" (even) without distribution: the network service being directly accessible is a sufficient condition and the distribution not a necessary one (it is also a sufficient condition though).

Distribution is network protocol which they claim copyright over. It only covers outside distribution and can't cover standardized protocols and formats because they don't own the copyright on those. If postgres was AGPL, they can't claim that ANSI SQL triggers copyright because ANSI SQL is owned by INCITS.

I have hard time understanding your comment, and even your point actually.

Distribution is distribution: sharing the binary / source code of the thing.

Network protocol are not involved at all. Direct network connection to the software from the end-user is.

If a particular implementation of ANSI SQL was AGPL, and you modified and used this particular implementation and exposed it to the world, you would need to redistribute the code of this particular implementation.

But that does not change anything about ANSI SQL or about any other implementation of ANSI SQL.

Protocols aren't copyrightable.

This isn't entirely correct, the trigger is on modification of the source code, the network accessibility is a sub-condition of that trigger.