If you consider restricting operations on your data close to the storage layer, you can imagine wrapping DB access with an app exposing business-specific API, and route all your actual code through that API. Doesn't seem like an unreasonable design to me - particularly, if the same database is used by multiple applications. But if you do that, it may make sense to just put the API inside the RDBMS - giving you one networked software component less to manage.
(I've done work on a project using lots of stored procedures only once, and my tasks were unrelated - so I have no practical experience here. But through this discussion, I think I'm starting to understand why enterprise projects are anecdotally so in love with stored procedures.)