I imagine, since SQLite does not connect over the network but is just part of the program, the permission model is "if the process is allowed to read the file,

I imagine, since SQLite does not connect over the network but is just part of the program, the permission model is "if the process is allowed to read the file, it can do things". That would probably boil down to "code execution on the machine means access to the DB". And that sounds pretty reasonable to me.