If you flip the "private" flag it would change the infohash of the torrent. The "private" flag is part of the info block in the torrent file's data. With an infohash mismatch between the two peers no download would happen.

Obviously after a non-compliant party to the transfer has fully downloaded the file(s) it can do whatever it wants with it afterwards… flip any flags and share via DHT, etc.

I recently shared some —more or less— private data to someone else via BitTorrent. We just used DHT for convenience. It took like 15 minutes for other random peers to pop into the transfer. All of those random peers just fetched the meta data. And indeed, a check on btdig confirmed the whole metadata (file names, file sizes, etc.) leaked. So there's a lot of DHT network scanning going on for sure. It was rather fascinating. No actual data was downloaded/leaked at least.