I did see a full copy of the SQLite amalgamation file in the FDB codebase, but you're probably right that they might be using internal APIs.
I'm still skeptical of the "tremendous performance penalty" you'd suffer from using SQLite. Just because you do fewer things doesn't necessarily mean you're faster at doing them. I've hit ~120,000 inserts/sec on SQLite without weakening any of it's durability guarantees. If you play fast and loose with fsync and WAL, I'm sure you can squeeze out even more performance.
I can also think of use-cases where you don't want the write amplification that comes with RocksDB or the memory constraints of LMDB.