I didn't find much in the way of clear and direct support for my statement about ffmpeg being built into mythtv, but I did find a couple of references strongly alluding to it.
There's this thread here on Phoronix, especially the second page:
I wish I'd seen that a long time ago, as it seems to speak directly to my current problems(I'm trying to playback smooth 1080P on a 780G board with onboard hd3200 GPU and 2.6 GHz 5050E processor). Sounds like I'm asking for trouble to start with.
And then there's this thread from July on a Mythtv developer mailing list: