Sending payments to fake addresses provides a way to broadcast short encoded and optionally encrypted unalterable messages to the world anonymously. Have security codes for the organization committing genocide, but scared you'll be killed if the publisher accidentally reveals your identity?

Publish them with Bitcoin.

That is an interesting application of Bitcoins that I hadn't thought of. Sending 0.0000001 BTC to some "trigger" address to detonate some weapon or to trigger a bot/virus to send a simple (even "complex") message when the value is received. I could think of several "covert" applications to something of that nature, and it would be difficult to trace the origin of that transmission too.
Not really any different from the classified ad.