You are correct, rtMedia does require either FFMPEG or Transcoder to play videos uploaded from an iPhone.
FFMPEG requires you to rent a media server and set it up properly. It is a completely "private" set up as both the servers are owned by you.
Transcoder only requires you to install a plugin and get a subscription. Your videos will be transferred to our servers, transcoded, and sent back. We take privacy very seriously.
Let me know if you have any further questions.