If clients access the database directly, then the database is now the server. You haven't removed the server, you've just moved it.
You're basically describing, for example, a Ember/Android/iOS + Rails + Postgres app. Logic lives in the client (Ember/Android/iOS). Data + Authorization lives in Rails + Postgres. And the Rails part of that is really not doing much. It's deciding if a request is allowed, then serializing or deserializing data from the database. I guess you can do that in the dbms, but you still need to do that somewhere.