Then by your definition, SQLite isn't open-source because it's a code dump with a license, but outsiders are not allowed to participate in shaping (the official copy of) the code.
It can generate plausible code because the examples are already in the training set, the documentation, the how-to-write-a-database, other databases, etc.
But unless you could write SQLite yourself it will be hard to specify a good one and to get the generator to produce a correct implementation.
The latter technically doesn't prevent anyone making money off it, but in practice it does (other than nominal fees).
That alone is a massive difference.