Yes, that's right. In fact, ZFS w/ encryption gives you two Merkle hash trees, one using a hash function and using a MAC. SQLite3 could do this, but it would have to change its database format fairly radically.

A SQLite3 VFS could, maybe, store additional metadata on the side knowing the SQLite3 database file format, I suppose. But if you really want this it's best to do it in the database itself.