If you have a lot of public documents to be shared across users, you can put it in a separate “common” database. Then you have a user specific private database for each user for documents that are sensitive. Especially if the number of public documents are large , wouldn’t make much sense to sync them down for every user of the app.
It looks like this is what you were proposing initially. Not sure I understand what the concern is. As long as you don’t expect to query across the databases, it should be fine.
Of course, if these public documents are known upfront, then you can load it using pre-built database as suggested above, but then again, if you have many users sharing the app on the device, you will have redundant data .