Actually, many RDBMSs (postgres included) provide security at the command, relation (table/view), and column level.
With that, and appropriate view definitions and triggers, you can essentially as fine-grained permissions as you'd like. We manage this all client side because while much of the theory of this has been around for servers and held up as the ideal model since very early in the RDBMS era, a lot of the necessary features were not implemented in many servers (or implemented so wildly inconsistently between servers as to make practical, rather than theoretical, knowledge sharing in the community difficult.) That's less true now, though it still requires implementation-specific knowledge for the SQL implementation you are using.
but this could be a moot point as long as db communication is only done server-side so it can be behind company firewall anyway -- after all, isn't that why the current db security model works? No one should EVER post ajax to the db, essentially. & i dont think anyone is suggesting that, i hope
So if I had insert and delete permissions on the Hacker News comments table to insert or delete my own posts, I could insert and delete every user's posts.
It's possible to imagine hacks that might work around this problem (e.g. comments-table-per-user, or liberal use of stored procedures) but none of them sound like particularly good ideas.